You really, really don't want spoilers for this movie. It's one of the few movies where I can say that without hesitation.
Taelorn, Firefly is effectively a space western. It involves the crew of a Firefly-class spaceship - "Serenity" - set in the future in another solar system. A Sino-Anglo (Chinese-American) Alliance controls the majority of the system, having beaten the Independents ("Browncoats") in a nasty war a few years back.
The captain of Firefly is a former soldier named Malcolm Reynolds. His crew is a pilot (Wash), his second in command (Zoe), an enforcer/tough guy (Jayne), and a mechanic (KayLee). In the TV show they pick up some passengers who stay with them, a Shepherd (or Preacher) named Book and a young doctor (Simon) and his sister River. It turns out that River is wanted by the Alliance - BADLY. She was being experimented on, and no one is quite sure what was done to her... but it has made her psychotic, and possibly very deadly. There's also a professional courtesan, Inarra, who uses a shuttle on the ship as her base for visiting clients.
The TV show is about their attempts to survive on the fringe of occupied planets, working shady deals and dealing with the Alliance hunting them. The movie deals more directly with what was done to River, and why.
Cast from left to right:
Inarra (companion), River (crazy passenger), Wash (pilot), Simon (doctor), KayLee (mechanic), Book (Shepherd), Jayne (tough guy), Zoe (2nd officer). Seated: Cptn Mal Reynolds.