This is the Prior family: Mrs Prior, Mr Prior, Caleb Prior and his sister, Beatrice Prior. Caleb and Beatrice are both 16 years old, and are about to go to the Choosing Ceremony.
After Caleb chooses Erudite, Beatrice isn't sure what to pick, because she is Divergent, meaning she can choose from any of the factions. However, in the end, Beatrice chooses Dauntless, the faction of the brave.
Beatrice decides that she should change her name to Tris, and she meets a new friend, Christina from Candor. They also meet their Initiation Instructors, Four and Eric.
Eric doesn't like Christina, and makes her hang over the Chasm for 5 minutes while the other Initiates watch as part of Initiation.