The super super short, Tweetable plot summary is: "Young woman in weird future leaves her family for exciting life, learns it's hard, and ruins villain's plan to destroy government." Huzzah. 130 characters—and they said it couldn't be done.
The longer, but still short summary goes a little something like this: Beatrice Prior lives in a future version of Chicago where there are five distinct factions. Each faction thinks one virtue is best: Dauntless think bravery is keen, Erudite love knowledge, Abnegation is pro-self-sacrifice, Amity hearts friendship, and Candor is into telling it like it is. Beatrice grew up in an Abnegation family. But when she turns 16, she decides to join Dauntless—partly because they're cool (tattoos, piercing, leather jackets, love of Wuthering Heights); partly because she doesn't feel selfless enough to be a good Abnegation; and partly because her test result showed that she was Divergent, meaning she doesn't really fit in with any one faction.
But joining Dauntless isn't just about showing up and saying "take me." All the initiates have to train and compete to get into the faction. Along the way, Beatrice takes a new nickname—Tris—and meets a range of people. There are new friends like Al, Will, and Christina; new enemies like Peter and his evil minions; and new teachers, like the scary Eric and the hot Four. Tris has to compete to get into Dauntless, all while hiding that she's really Divergent. There's blood, violence, and some kissing (between her and Four). So, pretty much the usual high school experience.
Then, Tris figures out that the Erudite faction wants to overthrow the Abnegation government. And they're going to do so by mind-controlling the Dauntless army. But Tris doesn't get brainwashed (because she's Divergent), so she destroys the villain's plan, and rescues everyone. Except for her mom and dad, who die to help her. Bonus: the book ends with the city in complete chaos, so it's time to pick up the sequel.