The Ruling Council was a group formed by the Dominion after it took over Deep Space 9 in late 2373.
After Weyoun had acquiesced to Odo's request to again make his deputies responsible for security on the promenade, he in turn asked Odo to become part of the station's ruling council along with himself and Gul Dukat. Kira Nerys was skeptical about this, since Odo's presence on the council validated Dominion control. (DS9: "A Time to Stand")
Jake Sisko asked Odo a similar question in an interview a little later, to which Odo replied that the Dominion didn't need his validation. (DS9: "Rocks and Shoals")
After Jake, Rom and Kira had caused a brawl between the Cardassians and Jem'Hadar at Quark's, Odo told her that while he spent his time on the council trying to protect Bajor, she was causing trouble by such actions. Kira then told him that maybe he shouldn't sit on the council when running the station smoothly made him forget the ongoing Dominion War. Later on, a council meeting was interrupted by the Female Changeling. (DS9: "Behind the Lines")
When the Changeling and Odo spent time linked together in his quarters, Odo missed a meeting of the council. When he wanted to leave for this meeting, she told Odo the meeting had been three days ago, which made him realize how much he had lost track of time. (DS9: "Favor the Bold")