Dr. Aurelius was a rebel doctor who was to take care of Katniss Everdeen during her stay in District 13. Dr. Aurelius was native to 13 and was happy to get Katniss as his patient, as she would not cooperate with him exactly, so he saw his sessions with her to be opportunities to take naps to make up for all his sleepless nights during the war.
Dr. Aurelius was also the doctor who was heading the study on Peeta's hijacking, sampling his memories with archived footage of his past with Katniss, his family, even bringing in some witnesses to help him regain his old thoughts. Though most of Dr. Aurelius' actions did not seem to make a difference as Peeta's recovery, only helped when he was with Katniss himself in person, not through the doctor's methods.
It is mentioned that Dr. Aurelius is a head doctor. He comes up with the theory that Katniss has become a mental, rather than a physical, Avox after seeing her sister, Prim, die. Other doctors were confused when she doesn't talk, and tests are conducted on Katniss' vocal cords, showing she should be able to speak.
After Katniss assassinated President Coin, Dr. Aurelius was summoned to her trial where he presented her as a "hopeless, shell-shocked lunatic" to save her from facing execution at the hands of District 13's government. In the end she was sentenced to being confined to the ruins of District 12 and she had to keep in contact with Dr. Aurelius to monitor her "mental illness." As Katniss wasted months in 12, Dr. Aurelius covered for her not calling by making up fake records and pretending to be treating her until she eventually did contact him.