The In many-worlds, the subjective appearance of wavefunction collapse is explained by the mechanism of quantum decoherence, and this is supposed to resolve all of the correlation paradoxes of quantum theory, such as the EPR paradox and Schrödinger's cat, since every possible outcome of every event defines or exists in its own "history" or "world". (Click link for more details) of quantum mechanics. Linked at the end of this post is a fairly heady explanation of this extraordinarily complex idea. But what it boils down to is that every possibility exists in an infinite number of dimensions.
Simple right? Of course not.
We exist in just one, of an infinite number of dimensions. Every choice we make guides how our specific version of our dimension plays out for us and others that share our specific dimension. However, since quantum mechanics states that every possible state of a particle exists, we just don't know what state it is in until we observe it, the other states don't vanish... we just don't see them. The other states exist in alternate versions of reality. Other dimensions. Other worlds.
The practical result of this is that there exists a world in which you ate fruit for breakfast this morning instead of that oh-so nutritious doughnut, or you live in a different country, or you are different sex, or a world where Hitler won, or the United States never won it's Independence.... anything that could have happened has happened and will happen in some world somewhere.
They key idea here is that while all these worlds exist, we can only directly observe and interact with a single one. Like a radio built pre-tuned a single station. But no radio is perfect!
The original relative state formulation is due to Hugh Everett in 1957. Later, this formulation was popularized and renamed many-worlds by Bryce Seligman DeWitt in the 1960s and 1970s. The decoherence approaches to interpreting quantum theory have been further explored and developed, becoming quite popular.