The Military Guild is one of the guilds present in Kryptonian society. The guild's purpose is to defend New Krypton (And formerly old Krypton as well, presumably) from internal and external hostile forces. The current head of the military guild is General Zod.
The Military Guild is one of the established and most important of the Kryptonian guild organizations. In the years when Krypton was a conquering race, the Kryptonian military was led by Admiral Dru-Zod the First who commanded entire fleets of ships, seeking out world ripe for conquest.  In later years, the Kryptonian Defense Council was led by Zod's descendent, also named Dru-Zod who achieved the rank of General.
General Zod gained prominence in the guild for his heroic, though futile, efforts to protect the city of Kandor from being appropriated by the alien conqueror, Brainiac.  Zod lost credibility however when he defected from the Kryptonian Defense Council, along with his wife Ursa, after they had been instructed to arrest scientist Jor-El after the latter had made sensationalistic claims of Krypton's pending destruction. By siding with Jor-El, Zod, Ursa and the former scientist Non were arrested and tried for acts of sedition. They were sentenced to spend eternity in the Phantom Zone, a limbo realm where they would continue to exist as disembodied wraiths. 
Years later, the Earth-based Kryptonian hero Superman liberated the stolen city of Kandor from Brainiac's head ship. Restored to it's proper size on Earth, those who survived their home world's destruction now had a second chance at life. Following the murder of Kandorian leader Zor-El, his widow Alura re-established the military guild so that they could defend themselves against those whom they felt were a threat. Zod was pardoned for his crimes and he was freed from the Phantom Zone. Alura re-established his rank and placed him in command of the new military Guild. It was at this time that Alura launched the entire city from Earth taking a geosynchronous position on the opposite side of Earth's orbit.
Superman was uncomfortable with the thought of Zod and his followers given free reign in a yellow-star system, so he flew to New Krypton to keep an eye on them. Alura told her nephew that if he were to remain on New Krypton, then he would be required to join one of the guild houses. Distressed by how things were being handled on this new world, Superman refused, so Alura placed him in the military guild under Zod's command. General Zod assigned Superman to take command of the Red Shard squadron. 
In addition to the Red Shard and Black Zero units, the Kryptonian Military Guild also maintained an espionage division led by Zod's wife Ursa. This involved seeding the planet Earth with Kryptonian sleeper agents who took up human guises and insinuated themselves into positions of power. One of these agents was a man named Tor-An who had adopted the guise of industrialist David Carter. Two masked Kryptonian heroes, Thara Ak-Var and Lor-Zod (son of Zod and Ursa) assumed the aliases Flamebird and Nightwing and began hunting down and exposing these sleeper agents. This invariably brought them into conflict with Ursa whom they fought at Superman's abandoned Fortress of Solitude.