The Council of Twelve was the ruling body that governs Krypton.
During the Krypton-Shi'ar War, the Council was considered by some of their peers and critics of becoming stagnate; among the most outspoken critic was General Dru-Zod, who grown frustrated by the Council's handling of the war, and eventually conspired a coup to overthrow the Council. However, the coup didn't came due to the siege that led to the death of Zod's lover, Ursa, and forcing the general to refocus his attention on the Shi'ar.
Following the war, the Council was responsible in carrying out General Zod's trial for war crimes against the Shi'ar in times of peace and banished him to the Phantom Zone. The Council was ultimately dissolved with the destruction of Krypton.
The Council of Twelve is apparently based on the Science Council from the Superman comics.