A setting where our comfy material world is just the tip of an iceberg, the very top layer of many; our puny human senses are simply not trained to perceive the rest of them. With certain magical rituals, you can move down into deeper layers... but there are things down there you might not wanna meet.
In a Layered World, several dimensions coexist in space and time. When you move onto deeper layers, you are usually capable of limited perception and interaction with the normal world but never vice versa, though magical sight may allow you to look down a layer or two. Also, each new layer often features slightly different laws of physics: you can gain the ability to walk through material walls, a speed boost, and even new powers, though these usually come at a price. Also, events in one world have an effect on attuned events in the other a la Synchronization or Fisher Kingdom.
The rule of thumb to recognize a Layered World is to look for characters saying things like "This place corresponds to some other place on another layer".
See also Recursive Reality and World Tree. For the physical, non-dimension spanning variant, see Hollow Earth. For the video game gameplay subtrope see Dual-World Gameplay.
In Mahou Sensei Negima!, the Magic World is like this. The Magic World is in Another Dimension that is layered on top of Mars.
One interpretation of the Black★Rock Shooter OAV is that both "normal" story and the Otherworld plot are the same event at the same time. Two friends dealing with loneliness and jealousy in one world are a Magical Girl fighting a possessed Dark Magical Girl in the Other at the same time.
Far, far more apparent in the Black★Rock Shooter TV series.
The universe of Slayers has an astral plane, in which the spiritual projections of mortals exist. Contrariwise, the (already very powerful) physical manifestations of supernatural creatures like demons can best be described as a mere projection of their astral body. Bundled together, said universe is but one of four parallel worlds separated by the golden sea of chaos, A.K.A. The Lord of Nightmares.
The world of Bobobo-bo Bo-bobo is like this, with the material world, along with multiple dark worlds (including one that acts as a Tailor-Made Prison for the emperor's brother, and a Bizarro Universe with an evil Bo-bobo and Beauty) and lots of bizarre, nonsensical mental worlds.
Fights in Il Sole penetra le illusioni take place in a weird approximation of what's going on in the real world. For the most part, this means that the Daemonia take the form of whatever they're manipulating, so the heroes can prevent more damage by blocking it's strikes, binding it, etc.
A Certain Magical Index: According to Tsuchimikado Motoharu, Heaven and Hell both exist in the exact same location as the physical plane, only at "different wavelengths", with Heaven being a higher frequency, and Hell a lower frequency. Humans of the world can detect neither, just as the otherworldly denizens cannot detect the opposite realm and its inhabitants. Only when angels and demons go into the realm in between, the physical world of the living, that the denizens can detect each other.
The various works in the Digimon franchise have at minimum the mundane world and cyberspace in the form of the Digital World. Digimon Adventure and Digimon Universe Applimonsters both have the Internet as a separate cyberspace dimension in itself. Many Digimon settings also have various other dimensions and in-between worlds with varying degrees of association with the local cyberspace such as the Dark Ocean, the DigiQuartz, and the AR-Fields. When Dimensions Collide is one of many consequences of these wildly different places coexisting.
In Inception, the protagonists use the concept of layers to plant an idea into someone's head. They kidnap him in a dream, rescue him in a Dream Within a Dream, team up with him in a dream within that dream... Which is necessary as for the inception to truly work it needs to be planted very deeply in the target's subconscious so that they will believe that it's their own idea.
Night Watch features the Twilight, a seven-layered reality accessible to sorcerers. Each level makes you incorporeal at higher levels (though you can still see and interact with objects and people in them) and gives you a speed boost, but also continuously absorbs your life energy until you either leave or are dead.
The Deverry Cycle has an ethereal plane (or astral plane, can't recall the terminology) that works like the D&D one.
The Bartimaeus Trilogy. The rules are never fully laid out and are sometimes inconsistent (one description in Amulet of Samarkand suggests physical objects are present on all layers, but in The Golems Eye a skeleton is explicitly not visible on any layer other than the 1st; Bartimaeus cannot change his true form on the 7th layer yet shrinks himself to avoid being crushed by a magical cage present on all layers). There are 7 layers of reality (though a theoretical 8th one is mentioned). Every spirit and spell is truly on one of the layers, and in case of spirits extends down to the first, although they can change their form on the lower layers; they can also perceive the layers they are on, with the exception of observer imps, who are on the 2nd layer yet see all of them. Humans and other living creatures are visible on all layers but can perceive only the first, although magical lenses show up to the 3rd layer clearly and 4th vaguely, and cats can perceive the 2nd. Ability to see higher layers seems affected by distance as in Bartimaeus comments at one point his disguise should hold up on all layers from far enough away.
The Nevernever in The Dresden Files is a reality layer underlying our common reality. Although the laws of common physics don't apply to it, the geography of Faerie (the closest part of Nevernever to real world) is such that you can, for instance, enter it in one place, then exit it in another, bypassing any defenses or traps set in real world. You can also directly affect the real world from the Nevernever (though not the other way around), as an angry ghost in the beginning of Grave Peril demonstrates.
It's not that people in the real world can't affect the Nevernever, rather that most denizens of reality lack the juice. It takes Faerie Queens, über-ghosts, or a seriously pissed-off wizard to send something through.
From Beyond by H. P. Lovecraft. The main character's acquaintance invents a machine that makes it possible to see the creatures that live in the different layers, but unfortunately, it works both ways. And given this is a Cosmic Horror universe, this is a very bad thing.
Shriek: An Afterword features fungoid spectacles that at low settings let the wearer see the marks of the Grey Caps' influence, but at higher settings are implied to peel back everything insufficiently real. Wearing them on such a high setting can make you catatonic for notable periods of time.
In Stephen King's Insomnia, Ralph Roberts is afflicted with the eponymous disorder, and as time goes by, he becomes able to use a wide variety of abilities. He is able to see the life auras of the people in his town, as well as differentiate sick and well people. He is also able to absorb these auras from people to replenish his own. He also becomes able to see little bald doctors who represent the Purpose(ful) and Random deaths of people. In time, he and his companion are able to rise high into the layers of the world, becoming invisible to people in the process. The downsides are that the higher they go, the faster time passes, and that there are things of a malevolent nature in the layers. Like the Crimson King, for example.
In K.K. Savage's science fiction novel Nation of the Third Eye, there are seven different dimensions. Some of these are physical, while others are astral. Those in the higher dimensions can see everything in the lower dimensions, but not the other way around.
The World of Tiers takes the form of a world-sized tower of Babel, just that the continent-sized layers (tiers) are way wider than they are tall. And the top layer has a Lord of Creation's palace on it.
Dungeons & Dragons cosmology has this with Border Ethereal Planes. A Border Ethereal Plane is an extra plane attached to Prime Material one, from which you can see and interact (via magic, not physically) with the contents of the Prime Material Plane. An object or person in the BEP is not visible or tangible in the PMP, so ethereal traveler can just walk through the normal prime walls. On the downside, ethereal can be seen by some people... including medusae and basilisks — and prime walls don't block this either.
In the magical theory of the Forgotten Realms, the Demiplane of Shadows has Shadow Fringe and Deep much like the Ethereal Plane has Border and Deep Ethereal. I.e. the Fringe is linked to every shadow in the given world, but being made of shadows, it's severely distorted. It's used almost exclusively for shadow-walking.
The Birthright setting had the Shadow World. Halflings originally came from there and could return if necessary.
The Ravenloft setting's Border Ethereal is more tangible than most, as a phenomenon called "ethereal resonance" allows ambient emotion in the Material plane to impose mood-appropriate motifs upon the Ether. Places where the Ethereal has been permeated by darker emotions can become sinkholes of evil, where malign forces fester and grow even nastier than is usual for the Land of Mists.
The Old World of Darkness has the Shadowlands and the Umbra (which also just means "shadow"), each of which is Another Dimension that overlaps with the "real world", representing the dead and living spirit of the world respectively. The Shadowlands is where Wraiths typically reside; it looks like the real world, only aging, decayed, and destroyed. Later, after a cataclysmic soul storm, the Shadowlands look more like the real world After the End (and is correspondingly now called "The Wasteland"). The Umbra is the world of living spirits, where metaphysics sets the rules and the inner nature of things from the physical plane is reflected. The Umbra itself contains multiple layers and even sub-realms, but the further one goes from the Penumbra (the first layer which reflects the physical world most closely) the harder it is to get back, the more dangerous the residents become, and the weirder things get.
Of the various dimensions that converge on the New World of Darkness, the Shadow, the Spirit World, is the one that best fits this trope, being the spiritual reflection of the material world.
And now, we have the Underworld, which works a hell of a lot like this. When you first enter, you're in the Autochthonous Depths, the area of the Underworld closest to the surface. After that lie the various Rivers, which take either power or sacrifice to cross, and after each one lie several Dead Dominions which go deeper and deeper into the Underworld.
GURPS Cabal features a world divided into four layers, based on kabbalistic cosmology: Assiah is the material world, Yetzirah the world of spirits, Briah the world of deities and archetypal entities, and Atziluth is the home of capital-G God.
The JAGS Wonderland setting uses this. Our reality is just the top level of a set of 8 "chessboards", which get weirder and more dangerous the deeper you go. While "down the rabbit hole," you could meet the Red Queen, the Mad Hatter, and other beings from the Lewis Carroll story.
Ars Magica has Regio, which are localized versions of this — alternative layered realities that only exist in one limited area.
In Dead Inside, the "real world" is just the outer shell of reality, wrapped around the Spirit World, which is itself wrapped around the Source. These layers of reality act as buffers protecting the Source from the Void outside reality. It's possible for characters to become living (or technically, undying) cracks in the shell of reality by losing every last scrap of their souls and becoming a channel for the Void.
The Night Bane setting has multiple layers to it. One in the form of the Nightlands. The Nightlands are a reflection of the real world, and is overall ruled over by the Night Lords. There is also the Astral Plane, which itself has three levels. The first is endless mists that is considered the surface, the second level where one can find the denizens, various realms, and cities made of spirit energy, and the last level known as the the Void which is home to Demon Locusts that want to consume...everything, as well as various mysteries such as Void Ships and powerful artifacts. Then you have the Dream Stream, which is...strange to put it mildly. Being the realm of dreams and nightmares, one can run into all kinds of things in it. In addition, because of the way the realm works, what happens in it can/will affect you and people in the real world who are asleep.
Within the World of Warcraft universe, there exist several dimensions in addition to the main one. The most well known of these is the Emerald Dream which is the spiritual blueprint to how Azeroth would have looked like without mortal interference and is where druids go to train their abilities. The next four planes of existence are the Elemental Planes which were created to imprison Azeroth's powerful elementals from wreaking havoc on the planet's surface. Azeroth seems to have several versions of the afterlife; there is the normal afterlife which known simply as the Shadowlands where souls can be easily ressurected, the Halls of Valor where vykrul warriors go after they die in battle, its polar opposite the Maw of Souls, and a black void where the most damned spirits go after they die.
The Mega Man Star Force series has the EM world, which consists of the EM waves of the normal universe. Geo Stelar can see it from the normal world with his special goggles. To get in, he has to find a portal and become Mega Man.
Silent Hill is a many-layered world, which The Movie is most explicit in showing.
In Silent Hill the film, there's the real world, where the husband and detective are; there's "ashy" Silent Hill, where Rose and Sybill end up, which is populated by monsters and trapped ghosts of cultists. Then there's the "air raid siren" Dark World, which has more and tougher monsters and is generally nightmarish and near impossible to survive in for long.
Eversion allows you to "evert" at several points (and forcibly everts you on occasion). Eversion is basically moving up or down a layer, which all have different properties, such as solid clouds, time stop, hazardous plants, etc. There are eight layers to this world, and only the top three layers are "friendly". As you evert further and further, the world gets darker and darker until it resembles something rather hellish.
The PC adventure game Torin's Passage takes place on a layered planet. The protagonist starts out on the surface but must journey through the "lands below", different worlds on different levels below the surface, in order to save his parents from an evil sorceress.
The World Ends with You's cosmology involves multiple "frequencies." The game takes place in the Underground, which is a slightly higher frequency than the Realground (the frequency everyday life takes place in), and as a result the Realground can be seen (and to some extent interacted with) from the Underground, but the Underground isn't visible from the Realground. Reapers are able to change their frequency to move between the Realground and Underground at will, but cannot use their powers in the Realground. Angels and the Composer naturally live on higher frequencies; coming down appears to limit their powers somewhat. The Noise are a rather strange case; they exist on their own frequency that's both on and in between the Underground and Realground, which also exists in two separate spaces. And then there's also the imaginary number plane you come across in Pork City, which is described as "a parallel plane a fraction away from the world Noise inhabit" and has no further explanation.
Trilby's Notes from the Chzo Mythos does this; it waits for map transition before randomly shifting you to the bad world.
Mighty Flip Champs! for DSiWare (and PSP minis) is all about solving puzzles by flipping from one reality to the next.
Wolfenstein game introduces The Veil an intermediate realm between this world and that of the Black Sun. Viewing objects through the Veil may be different than viewing it normally, such as brand new fighter planes appearing derelict to the point of crumbling.
The Spectral Realm in the Legacy of Kain games is a good example of a two-layered world.
Star Control has Realspace as where we live. "Above" Realspace is Hyperspace, used for interstellar travel, and Quasispace, used for really fast interstellar travel and the place where the human friendly Arilou live. "Below" are... well you don't want to go *below*. The Androsynth appearently looked *below*, and now there are no Androsynth. Only Orz.
Even the Orz, who are implied to be native to *below*, say that it's a terrible place where they were in constant *pain*. Hence why they like Realspace so much.
In Time Fcuk, the majority of levels have 2 layers although many user-made levels can have up to 3 which the player interacts with.
Bayonetta does this, with the character herself in Purgatorio, able to see the (semitransparent) humans in reality.
In the world of Fate/stay night and Nasuverse in general, there exists the Reverse Side of The World, a realm that exists above and below the physical world and the home of Phantasmal Beasts after the decline of Age of Gods. It is devoid of humans although one can reach it after death with very small odds. It is also where the realm of Avalon is located. It is separated from the physical world by the pillar of light which is the true nature of the Holy Spear Rhongomyniad. Several lines indicate there are other layers of existence beneath even the Reverse Side. The crux of Fate/Grand Order's second storyline is that an extraterrestrial God is attempting to "stitch" a new realm of reality over the current world using a similar process in order to be able to exist on it without issue, with the cost being humanity itself as we know it.
The Legend of Zelda games often feature the Dark World, which reflects the regular world in various ways; and in some games, you can affect one by acting in the other. The Dark World was originally a Spirit World that was corrupted by evil. The Legend of Zelda: Twilight Princess also introduces the Twilight World, which may be part of the Dark World or a different plane entirely.
Ghostbusters: The Video Game kind of touches upon this, especially in the Public Library section, whose second half takes place in the library's Gozerian configuration (one of millions of theoretical configurations). The game doesn't really go far enough, but then again, your job as the Recruit is to keep the dimensions separate.
In the Persona series, most demons and other such beings are located within the Collective Unconscious and the Sea of Souls, which are visited by the protagonists of the games in various forms.
The Submachine series, especially The Plan and to a lesser extent The Temple (other games mention the layers, but these two are the only ones where the player travels between them - unless that's what's happening in The Loop.) The Exit reveals that there are an infinite number of sublayers, which is why you can see evidence of other explorers, but never actually meet them.
There's the Astral, which is a Spirit World and a Dream World that have locations which basically correspond to locations in the Material World.
There's also a Cyberspace connecting all connected technology, although, airgapped technology may not be accessible.