The Quorum of Twelve, also known as "The Council of Twelve" or "The Council", is a group of politicians who gather together to make up the laws and practices for the people of The Twelve Colonies.
The seats are made up of one representative from each colony and are presided over by the President. Each representive as well as the President are elected to their positions.
After the destruction of the Twelve Colonies and the death of President Adar, Commander Adama of the planet Caprica was installed as interim leader of The Council operating under martial law. The council could still make laws and practices but Adama controlled the overall actions of the Council.
The council did try to take control again when The Eastern Alliance was taken into custody aboard the Galactica. But when the Alliance, along with Baltar and three Borellian Nomen try to escape and use the council as prisoners, the council gave control back to Adama.