"This idea was so uncomfortable that for decades scientists dismissed it, but in time parallel universes would make a spectacular comeback. This time they'd be different, they'd be even stranger than Elvis being alive. There's an old proverb that says: be careful what you wish for in case your wish comes true. The most fervent wish of physics has long been that it could find a single elegant theory which would sum up everything in our Universe. It was this dream which would lead unwittingly to the rediscovery of parallel universes. It's a dream which has driven the work of almost every physicist."
Physics Hidden in the dustier corners of the BBC's website is a transcript of Horizon's 2002 episode on Parallel Universes, which includes clear explanations for the concept or at least why it's become so important within physics for explaining the unexplainable: