The Council is the government for Citadel Space. The Three-- four, since humanity joined, biggest races on the galaxy each have a representative, they make the rules the rest of the galaxy plays to.

All the races have their own government and territory, but by and large they're part of the Citadel Government. They follow the rules, get protection, aid, trading agreements ...

I think a human on the Normandy called it "The U.N. on steroids," whatever that means.