The many-worlds interpretation (MWI) of Quantum Mechanics was first suggested by Hugh Everett in 1957. MWI assumes that the wavefunction of any object is not observer-dependent, obeys the standard wave equations at all times whether a measurement is being taken or not, and that the wavefunction is a real object in itself. That is, the observer has no special role and that there is no collapse of the wavefunction. This is totally at odds with the Copenhagen interpretation of quantum theory. In fact, at John Wheeler's suggestion, Everett went to Copenhagen and met with Niels Bohr, the "father" of the Copenhagen interpretation. It was, apparently, a disaster with neither man able to comprehend the other's stance. One colleague of Bohr's described Everett as an idiot, which was a little unreasonable!
In practice, this means that whenever there is an interaction, the wavefunction of the Universe branches into several paths; one for each possible outcome. This could be a macro event, I buy the shoes/I do not buy them, or an event at the quantum level, a particle decays/does not decay. As an example, consider the famous thought experiment of Schrödinger's cat. The Copenhagen interpretation tells us the cat is in a state of being alive-or-dead until an observer looks in the box and collapses the wave function. Many-worlds tells us that the universe splits into two; one where the cat is alive, the other where it is dead. In the first, the observer finds a live cat, in the second it is, unfortunately, a dead cat. Every possible outcome of every event exists within its own world, resulting in, perhaps, an infinite number of universes, representing every possible thing that could have happened since the Universe began.