The bartender says "We don't serve your kind." A neutrino walks into a bar.The idea here is that Henri Poincare invented a convention for clock synchronization in 1898 that used light signals. The premise was that light was the fastest possible communication. Einstein published the same scheme in his famous 1905 relativity paper, and denied that he had read anything by Poincare. Historians agree that Einstein read Poincare's 1902 book, and that the book references the 1898 paper, but they disagree about whether Einstein plagiarized the synchronization convention. If a neutrino could go faster than light, then it would seem to be going backwards in time, according to the light-synchronized clocks. If info could be somehow communicated to the past, then that would violate straightforward notions of causality. The joke is that the lines are out of order, and thus violating causality. Except that the joke does not make any sense. It should be the neutrino that is going backwards in time, not the bartender. A more sensible joke would be:
A neutrino walks out of a bar. The bartender says "We don't serve your kind."Of course it is still impossible to make sense out of causality violation. The basic problem is illustrated by science fiction plots where someone murders his own grandfather, or something like that. There are physicists who claim that certain scenarios for backwards time travel are not logically or physically impossible, but they are all far-fetched.
There is now a proposed explanation (criticized here) for the neutrinos. It argues that the GPS satellites do not have all of the necessary relativistic corrections. This would be very embarrassing to the GPS folks if true, but some sort of systematic error like this seems likely.
Today's Brewster Rockit comic has a nice illustration of a time travel paradox.