Max was a former Dauntless leader.
Max first appears right at the beginning of initiation, casually walking on the ledge of the rooftop the Dauntless had landed on after jumping from the train. He instructs the initiates of their next move, which is to jump off the roof, ahead of the members, into the entrance to the Dauntless compound, later giving way to Tris when she moves forward to jump first.
Max is later mentioned again by Eric to Four, wanting to check up on him and know if he is finally interested in the position he was being offered as a Dauntless leader. Four insists that he does not want it, and Eric says that he hopes Max gets the point and stops asking Four.
Later, Four also told Tris that Max was one of the leaders that changed the training methods of Dauntless to make them more competitive and brutal, to apparently test the initiates' strength, therefore changing the priorities of Dauntless as a whole. Max was also the one who appointed Eric as a leader under Jeanine Matthews' orders.
Max is also among the Dauntless leaders who watched the simulations during the third stage of initiation, and those who were not put under the simulation the attack on the Abnegation.
Max is sent by Jeanine as a representative to meet with Jack Kang, the Candor representative. Tris notices something off about the way he speaks, and soon realizes that Jeanine is in the area, telling Max what to say through an earpiece. As Tris and the others sneak away to try and locate Jeanine, Lynn strays from them and shoots Max in the chest.
After Tris Prior reveals the message, Jeanine Matthews orders Tris Prior and Tobias Eaton be killed. Max raises his gun, but the Factionless and Dauntless storm in, and Lynn (Edgar in the movie) shoots Max. Max survives his injury.
Max is put on trial, and is executed by Edgar.