Bizarre as the notion of a multiverse might seem, in a way it actually fits the progression through modern history of how humans view themselves and the universe.
As physicists Alexander Vilenkin and Max Tegmark noted in a 2011 Scientific American essay, people in western civilization have been successively more humbled as they've discovered the nature of reality. They started out thinking the earth was the center of everything. We learned that wasn't true, and that even our solar system was just a not particularly significant part of the Milky Way.
The multiverse would take that pattern to its logical extreme. If multiverses exist, that means that we're not special at all, because there are infinite versions of each of us.
But some think that we're just at the beginning of a mind-expanding trip. As Stanford University theoretical physicist Leonard Susskind has written, it could be that a couple of centuries from now, philosophers and scientists will look back on our time as "a golden age in which the narrow, provincial 20th century concept of the universe gave way to a bigger, better ... of mind-boggling proportions" [source: Vilenkin and Tegmark].