The opening sequence gives newcomers most of the backstory. The characters are introduced as much as they need be in the next sequence. If you've never seen the tv show, you'll like Serenity. A lot.
Damn close to a perfect movie. Even better: Damn close to a perfect science fiction movie.
And it's a movie, not a tv show. For those of you who pay attention to such things, watch the first sequence on Firefly, under the opening credits and beyond. Most of it is one long take. Joss Whedon is the director as well as the writer of the movie, and he's probably just made his reputation in the former as high as the latter.
Notice how back story gets filled in: The opening and denouement both use flashbacks that repeat. Notice how the characters are comfortable in their own skin. Whedon is famous for his dialog, and while there's not so much offhand humor there is a lot of character development. The sound and dialog are as important as the visuals.
Serenity works as both a continuation of the tv show and as a powerful standalone movie. Anyone reading this is likely to appreciate the movie more than the average mundane. Highly recommended. Here it is, and hour or so after leaving the theater and a few misgivings are surfacing. But very few. At the moment, on the Shockwave Radio Theater scale of 9 to 23, with 23 being top, I'd give Serenity about a 22.