The Council of Corellia is the top-management and power-making structure within The Organization, consisting of the 6 Operations Managers, Deputy Director, and Director, and makes all major decisions. The Council of Corellia is also in charge of electing the next Deputy Director and Director when either one of them die.
It is unclear how the name of the Council of Corellia came about, but many theorists suggest that the name came about during the early days of the Galactic Republic when The Organization's early power makers were concerned over the common Corellian government making decisions. As such, the Council of Corellia became a over-inflated egoistical sense of self-importance in how The Organization saw itself in terms of being able to sway Corellia one way or another in political decisions.
Regardless of how The Organization once saw itself, the Council of Corellia maintains very close ties with The Council and the House of Royal Intelligence.