There have been about a half dozen threads on this movie, with all sorts of explanations. Shouldn’t be too hard to search for one, and you’ll probably find links in it to all the others.
Anyway, here’s my take (it’s been about a year since I last saw the movie, so I might make a few mistakes here) Oh, and spoilers ahoy, if anyone reading this is concerned about that kind of thing.
Basically, for whatever reason, Donnie Darko has the ability to see in four dimensions: the three spatial dimensions, and time. The human brain isn’t really wired for that, though, and it alters what he sees into a form he can process. Namely, Frank in the bunny suit, telling him stuff.
In my view, what happens is God (or the Universe, or Kismet, or whatever) gives Donnie a choice: either the events of the movie play out as portrayed (his girlfriend gets run over, his mom and sister die in a plane crash, he murders Frank), or Donnie can sacrifice himself by staying in his bed and getting pulped by the jet engine. The catch, of course, is that whatever he chooses, no one else will ever know, because the alternate possibility never happens. Throughout the course of the movie, he gets all these psychic flashes about what’s going to happen, and then, at the very last, he’s given the chance to go back in time and prevent all this grief from happening, which he does. Actually, it appears that everyone is sent back in time, and they seem to remember the alternate timeline as some sort of super realistic dream, as evidenced by the scene of all the characters waking up just as Donnie dies and clearly reacting to experiences in the other time line (Frank holding his eye where he was shot, Patrick Swayze’s attack of conscience for being a pedo, etc.)
There’s a lot more going on, obviously, and I don’t remember all the details (need to see it again) and apparently, the movie’s creator has a commentary track on the DVD that explicitly refutes most of what I just typed. But what the hell does that guy know? I like my explanation better, and I’m sticking with it.