Many worlds says that quantum mechanics is all that there is, and all observed consequences can be predicted from the assumption that we, ourselves, are complex quantum mechanical systems. The prediction is that we coexist with superpositions of ourselves doing different things and cannot meaningfully interact with them. This seems weird to us, but is exactly what the theory predicts.
Consider Schroedinger's cat. We ask whether the cat is both alive and dead before we open the box. This puzzles us because that is what quantum mechanics predicts and that seems weird. Multiple worlds says that quantum mechanics holds, it remains both alive and dead AFTER we open the box, and while it seems weird, there is no actual contradiction anywhere.
So mathematically simple. Weird consequences. In perfect accord with our best theories and best experiments.
By contrast the Copenhagen interpretation says that there is a collapse somewhere even though there is no experimental evidence for it, and we have no theory about how it might happen. And the pilot-wave interpretation says that our best theories notwithstanding, the universe is something different and weird in a different way.