The Great Captains are the military generals for the nation-state of Krakoa. While the Quiet Council is a civil and political government, the Great Captains make war when necessary in the name of Krakoa and defend the borders from threats.
Cyclops is the Great Captain commander, first among equals, representing the X-Men. Magik is Great Captain of the Sextant, the academic habitats home to the younger generations of mutants. Bishop co-serves as Great Captain and Red Bishop, representing the Hellfire Trading Company. Gorgon is tasked specifically as Great Captain guarding the persons of the Quiet Council, particularly the August branch of Xavier, Magneto, and Apocalypse when they travel overseas.
Cyclops has since stepped down as Captain Commander due to his additional duties with the X-Men, and the Captains nominated Bishop as the new Commander. With Gorgon's difficulties following his death in Otherworld, Kwannon has replaced him as the fourth Captain.