<PERSON>'s Equivalence principle states that freefalling reference frames are equivalent to an inertial reference frame; or to put it another way, inertial accelerative effects are equivalent to gravitational effects. This thought experiment might help:
I step into an elevator in an Earth-based building, the door closes but the elevator stays still. A varies of senses tell me which way is "up". If I jump, I quickly land back on my feet. If I try to pick up my 30kg suitcase, I can feel its weight. Now, suppose I, along with the contents of the elevator, am instantly teleported to an identical elevator in a spaceship in deep space. If the spaceship is accelerating at 1 g in a direction parallel with my conception of "up", I will have no way of knowing whether the teleportation worked and I'm on the spaceship, or it failed and I rematerialised back in the Earth-based elevator. My sense of "up", my attempts to jump or to pick up the suitcase are all indifferentiable.
So long as it's at rest in relation to the building, the Earth-based elevator's acceleration towards the centre of the Earth at 1 g is resisted by mechanical forces, which I experience as the floor exerting an upwards force on me through my feet. In the spaceship, I experience an equivalent force through my feet due to the rocket engine propelling the floor "upwards".
Now, suppose I suddenly feel weightless. My stomach lurches and I feel like vomiting. 766
A little push of my toes sends me gently towards the ceiling. I panic and grab the suitcase handle, which slows my overall upwards trajectory but sends the suitcase towards the ceiling too, and my torso starts swinging in an arc. Did the rocket engine just cut out and I'm now in "free fall", or did the elevator cable snap and it's now falling at 9.8 $ms^{-2}$ (ignoring air resistance etc). For the moment at least, it's very hard to tell; perhaps I pick up that there's no faint vibration (the rocket thrusters), or perhaps I hear some scraping sounds (the elevator). I'll discover the truth in only a few seconds...
When I am in the elevator at rest, I don't feel any fictitious force pulling me back. Or do I?
In general relativity, gravity appears as a fictitious force; this is because GR attributes the apparent acceleration of gravity to the curvature of spacetime. You feel this fictitious force when you are in a non-inertial reference frame, e.g. "pulling you back" towards the floor in the elevator in an Earth-based building. You don't "feel" gravity in an inertial reference frame (e.g. when the elevator cable snapped) because in that frame there's no force acting on you. 393