Katniss's expert archery skills enable her to provide for her widowed mother and younger sister by supplementing their income with illegally procured meat. But when Katsa is chosen as an unwilling regional representative to The Games, a highly-anticipated, fight-to-the finish competition, her unusual skill becomes her only chance to survive.
Watch out for changing your characters' names in the middle of the synopsis. (Yes, you've just been reading Graceling, I know.) Don't say "fight to the finish" when you're just introducing the book to people-- this is a fight to the death, and it's important to bring that across.
Protecting herself in the competition is challenging. Deciding whether to protect other competitors is heart-breaking. As the cruelties of the Game grow more fierce, Katniss's anger at the vicious system escalates. Instead of killing her final competitor and friend, Katniss turns her energies to out-witting the system and forcing an ending with more than one survivor. Although she triumphs over the most vicious elements of the Game, she isn't happy; the self-knowledge she has gained is as alarming as it is enlightening. This dystopian tale looks backward to the age of gladiators and forward to what we may become.
Excellent job! You got all the most important pieces of this plot, didn't get sidetracked talking about the possible romantic implications (which may or may not come to fruit in a further book) and wrapped it all up in an easily-grasped, almost catchy way.