This film is based on the all too brief TV series Firefly. Between the series and the movie, there was also a three issue comic book miniseries called Serenity: Those Left Behind, to bridge the gap. It isn't particularly important to read the comics before you see the movie, but it certainly wouldn't hurt. The most important thing you get from them is that Inara and Book each left Serenity and went their separate ways. Anyway, the Alliance sends out an Operative to capture River. Meanwhile, the Serenity crew is doing a job when suddenly Reavers attack, and there's a big chase scene where they have to get back to the ship... which of course they do, but it's plenty dramatic. I would say their troubles were just beginning at this point, but of course their troubles actually began a hell of a long time ago. There are way more yet to come, though.
Here's the thing. Part of me wants to detail pretty much the whole series of events that transpire in the film, just leaving out a few of the biggest spoilers. But I really don't want to ruin anything for you, so it's probably better not to say much of anything specific at all. We see Book again, and Inara. River goes a little nuts at one point (okay, a lot nuts, but in a really kick-ass way), but also gets a clue that leads everyone to a deep, dark secret the Alliance has kept hidden, and then our heroes all have to try to expose the secret. The Operative keeps doing everything he can to stop them. There's a lot of fightin' an' killin' and all manner of unpleasantness. There's a lot of surprises. There's a lot of humor, and a lot of tragedy. At times it's terribly difficult to watch, but it's worth it. It instantly became one of my favorite movies ever. I really don't think I can explain it any better without spoiling it, you just have to see it. But hey, maybe after I watch it on DVD, I'll try to say more about it here. Or maybe not...
Also, you might want to check out my Avatar/Serenity trailer (which uses the audio from the trailer for this movie, and video clips from "Avatar: The Last Airbender").