The Gray Council is a secret society within the Jedi Order, they believe that the cycle of conflict, resolution, and reconstruction is what fuels Galactic Advancement and that the balance between Chaos and order must be maintained if progression is to thrive. They work in absolute secret never allying themselves with any faction. The history of the Council is something that only Council members are told, although it has likely been centuries. The Council consists of 9 members total divided into 3 triads, the Gray Triad, the Light Triad, and the Dark Triad. Each Triad has a leader, the Jedi Master of the Council, the Dark Lord of the Council, and the Grand Master of the Council (who also leads the Council as a whole). The leaders of each Triad form the Upper Council which is tasked with regulating competition amongst members and ensuring that it stays constructive.
While the Council is a major part of the organization it is far from the only part. Their is also a large compliment of Jedi Knights that have sworn themselves to the Gray Council, they are only the most promising or proven Jedi whose loyalty can be ensured or whose tongues can be silenced and even then none but Council members ever know the full extent of the resources and personnel available. Jedi are not the only ones employed by the Council, a host of puppet politicians, republic officials, and various others from throughout the galaxy are controlled often unknowingly through every and any means available.