It's basically software that works the way its authors think it should work, instead of trying to please everybody. That means a lot of people will not like it, but the ones that do will love it.
Rails is probably the canonical example of an opinionated framework: you do things their way, and everything is smooth. If you don't, you're in for some pain. But that's OK -- if you don't want to do things their way, you don't want to use Rails.
