In recent decades, the Many-Worlds Interpretation of quantum mechanics has become one of the most popular alternatives to the nearly century old "Copenhagen Interpretation".

Since the 1920s, the accepted understanding of quantum mechanics (how the universe behaves on the very smallest scales), has been the "Copenhagen Interpretation" named after Niels Bohr's Copenhagen Institute where the world's top physicists met to discuss the theory.  However, starting in the 1950s alternatives have been proposed, including Hugh Everett's "Many-Worlds Interpretation."

While both Copenhagen and Many-Worlds have at their core the same fundamental formulas, they differ in terms of how they apply them to our world.  Unlike classical physics, the equations quantum mechanics don't tell us exactly what will happen, instead they can only tell us the probability that some event will happen out of many possibilities.  The Copenhagen Interpretation says that all of those possibilities exist until the result is observed, and then just one of them (chosen at random) becomes real.  The Many-Worlds interpretation instead believes that all of those possibilities are equally real, just in different "worlds," popularly: alternate universes.

Its supporters argue that Many-Worlds is a simpler and more elegant interpretation, because it doesn't require any additional theories about "observation" or complex explanations of how we go from just possibilities to one real event.  Instead, Many-Worlds uses just the fundamental equation governing quantum mechanics and nothing more.
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