Note: this idea goes by many other names, one of which is the many-worlds hypothesis.
One of the possible interpretations of Quantum Mechanics. In this interpretation, every time a "decision" has to be made at the quantum level -- for instance, the spin of an electron is measured -- the Universe splits in two, and each of the possible outcomes of the decision actually happens. IANAPhysicist, but my understanding is that this is a compatible extension of the traditional Copenhagen Interpretation of QM.
Because of the storytelling possibilities, this interpretation of QM tends to get abused quite a bit in science fiction. There has been at least one episode of Star Trek: The Next Generation where a "quantum fissure" or some such anomaly made Worf start jumping between quantum universes. Also, the entire premise of Sliders is that it is somehow possible to create a bridge between quantum universes. In reality, the Many Worlds interpretation is one that cannot be verified experimentally, and is thus more of a philosophical proposition than a scientific theory.