The Ruling Council was the central government and judiciary body of the planet Krypton. The Council was composed of several of the eldest and most politically experienced members of Krypton's elite Houses and their dictations were respected by virtually all of Kryptonian society.
During the war with Black Zero, the Ruling Council began making preparations in accordance to Rao's prophecy. To preserve their race, they used technology created by Jor-El and planned to take the blood of Krypton's strongest so clones could be created on another planet should Krypton be destroyed. Jor-El opposed these plans because he knew that Earth's Yellow sun would give the Kryptonians unimaginable power and the humans would not stand a chance against them if they were exposed to Red or Silver K or if they were to turn evil so Jor-El stopped the experiment before being summoned before the Council. The Council agreed that Jor-El had committed an act of treason and sentenced him to death. Major Zod crashed the tribunal and pleaded that Jor-El's life be spared. The Council agreed, but only if Jor-El finished the experiment himself and included both his and Zod's blood samples in the Orb.
Kara and the Chronicles of Krypton
When General Zod began gathering armies in an attempt to take over Krypton, the Council inquired and the latter provoked a war with Zod, who planned to make himself absolute ruler of Krypton. Jor-El took charge of the defense of Krypton against Zod and his disciples, and created the Brain InterActive Construct based on Dax-Ur's designs to help the Council defeat Zod. Somehow, Zod was able to corrupt Brainiac's system and turn him against the Council and Jor-El. 
When Krypton began suffering from seismic tremors during the war, Jor-El suspected that his brother Zor-El was responsible by using Kandor's mine at full capacity and asked his fellow Council members to speak to Zor-El, who blamed the seismic tremors on Zod.
The Council managed to defeat and capture Zod, destroying his physical body and placing his spirit into the Phantom Zone. They subsequently found out about Zor-El's connection with Zod and informed Jor-El that he should contact his brother and tell him that they have caught Zod and that he can stop Kandor's mine from running at full capacity. Jor-El then told Zor-El that he was under arrest and locked him in the mine's control room, but Zor-El contacted Brainiac, who overrode the lockdown and re-initiated the countdown of Krypton's core, and managed to destroy Krypton.
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In the Comics
The Kryptonian Science Council was an assembly of esteemed scientists gathered together in the capital city of Kandor (and later in Kryptonopolis) to govern the progress of Krypton's technocratic bureaucracy. The assembly speaker was known as a Drygur and presided over a council of Molioms. Following the destruction of Krypton, the surviving Kryptonians forged a new life for themselves in both the bottle city of Kandor and Argo City. Each city established a new Science Council to govern their legislature.