The many-worlds interpretation is an interpretation of quantum mechanics.
It is also known as MWI, the relative state formulation, theory of the universal wavefunction, parallel universes, many-universes interpretation or just many worlds.
Many-worlds denies the objective reality of wavefunction collapse, instead explaining the subjective appearance of wavefunction collapse with the mechanism of quantum decoherence. Many-worlds claims to resolve all of the correlation paradoxes of quantum theory, such as the EPR paradox, since every possible outcome to every event defines or exists in its own "history" or "world." In layman's terms, this means that there is a very large, perhaps infinite, number of universes and that everything that could possibly happen, or could possibly have happened, in our universe (but doesn't) does happen in some other universe(s).
Proponents argue that MWI reconciles how we can perceive non-deterministic events (such as the random decay of a radioactive atom) with the deterministic equations of quantum physics. Prior to many worlds this had been viewed as a single "world-line". Many-worlds rather views it as a many-branched tree where every possible quantum event is realised.
The relative state formulation is due to Hugh Everett who formulated it in 1957. Later, this formulation was popularized and renamed many worlds by Bryce Seligman DeWitt in the 1960s and '70s. The decoherence approach to interpreting quantum theory has been further explored and developed becoming quite popular, taken as a class overall. MWI is one of many Multiverse hypotheses in physics and philosophy. It is currently considered a mainstream interpretation along with the other decoherence interpretations and the Copenhagen interpretation.The many worlds interpretation has, controversially, been seen by some as offering the possibility of deriving the Born rule and the appearance of quantum probabilities from simpler assumptions. In fact, this was first attempted by Everett and DeWitt in the 1950s. In a September 2007 conference David Wallace reported on what is claimed to be a proof by Deutsch and himself of the Born Rule starting from Everettian assumptions. The status of these arguments remains highly controversial, but it is fair to say that some theoretical physicists have taken them as supporting the case for parallel universes.