The idea is that Woody Allen's character, Dobel, is a time traveler who's come back to talk to his younger self (Jason Biggs's character, Falk) and break him out of bad relationships with his girlfriend, his manager, and his shrink, guiding him to a better life as a sitcom writer in LA. You could argue that the movie is just a metaphorical way for Woody to reflect on his life and think about how he could have changed things, and that it shouldn't be considered a literal plot device; there's certainly nothing in the movie to explicitly indicate that he's actually travelled through time. But there are a lot of little coincidences: a joke about quantum physics and time and space being the same thing, various references to time and prediction, and the cab driver at the end of the movie saying the same thing to Falk that Dobel said a cab driver said to him long ago ("it's like anything else"). I also like the idea that the reason Dobel has such a strange vocabulary (tergiversate, adventitious) is that language has evolved in the future so that these words are more commonplace. But even more things fit into place if you imagine that Dobel came from a specific apocalyptic future, and he's trying to warn Falk about increasing anti-Semitism, to teach him to fight back and take a stand against oppression (like smashing the car of the bullies who steal his parking space), and to arm him with a rifle and a survival kit and even get him out of New York altogether. Near the end of the movie there's a close-up of Falk typing something that Dobel said to him: the Nazi atrocities were so bad that if the entire human race were destroyed as a penalty it would be justified. The way this was emphasized in the movie seemed particularly odd to me while watching, which makes me think it really is some sort of intentional clue of what happens in the future timeline. One person brought up the possibility that Dobel was a ghost, Sixth Sense-style, who barely makes an impression on anyone but Falk, dropping the vase when handed to him, etc., but I think this is kind of a stretch. (Although it does make me think of his 1990 movie Alice, with magic powders of invisibility and insubstantiality.)
Anyway, check it out, it's running on HBO for the next couple weeks.