What does "jive", when referring to speech, mean? As in, "That just doesn't jive."?

picador is correct. I've always known the word jibe to have the meaning 'to agree or be consistent', as in "his appearance doesn't jibe with his claim to be a prominent lawyer". I think jive is used that way by people who don't know any better. They know the word jive already and think they're hearing the same word used a different way. Urban Dictionary is reflecting what people are saying lately, not proper English.