For the uninitiated, Firefly was a show created by Joss Whedon which aired on the Fox Television network from September to December 2002.
In a nutshell, Fox network producers showed the series out of its intended order so nothing flowed or made sense. It suffered from low ratings, and was canceled after only 14 episodes.
I could go on, but Wikipedia has it pretty well covered for the uninitiated.
The 8 minute video below shows things a tad out of order as well. First scene is basically the last, then the rest show River Tam as a young 15-something girl going from a youthful, brilliant girl to a psychotic potential killer due to government behavior modification experimentation.
The video is called The R. Tam Sessions and was released as a webisode leading to the release of the movie Serenity.
Joss Whedon plays the counselor, and of course Summer Glau is River Tam.