The Council of the Home is the governing body who first explains to Equality 7-2521 that there "are few offenses blacker than to fight with our brothers," no matter one's age or one's cause.
The Council of the Home is also the body who retains a sundial in its courtyard so it "can tell the hours of the day and when to ring the bell" to let everyone know when it is time to get up, to go to work, to eat lunch, to work again, to eat dinner, and to go to the Social Meeting.
Moreover, as Equality 7-2521 says,
Our body is betraying us, for the Council of the Home looks with suspicious upon us. it is not good to feel too much joy nor to be glad that our body lives.
Individuals are taught that they do not matter; what matters is the collective. Therefore, when Equality 7-2521 seems too happy or joyful or glad to be alive, he draws negative attention from the Council of the Home for his behavior.
The Council of the Home is also the body that questions Equality 7-2521 after he is caught. He loses track of time while in his tunnel and doesn't show up where he's supposed to be when he's supposed to be there. The Council asks him where he has been, and, when he refuses to tell them, the oldest member orders him to be taken to the "Palace of Corrective Detention" and "Lash[ed] . . . until they tell."
As a result of these four mentions of the Council of the Home, it appears to be something like a regulatory and governing body that deals with infractions and keeps time for the entire community.