The Council is the ruling government of The Citadel. One representative of each Council Race is selected to hold a seat in discussing matters of galactic importance. At the start of Mass Effect only 3 Races have seats on the council. Turians (bird people who sound like Willem DaFoe), Asari (blue lesbian race) and Salarians (big eyed paranoid alien thingies). The Turian representative is a typical Turian (racist, stereotypical and likes to moan at everything done by a human), the Asari representative looks like a twilek prostitute from a Star Wars cantina, and the Salarian representative who is just average.
At the end of Mass Effect the player can choose a representative for the human race (a wide choice between 2 potential candidates). The token black guy Captain Anderson, or the prick Ambassador Udina.