'ANBU' is short for 'Ansatsu Senjutsu Tokushu Butai' (Special Assassination and Tactical Squad). In TNR, ANBU squads are created and controlled by the kage, though the squad leader runs the actual squad.
The Kage creates the squad name and orders, and appoints a leader. (Usually, the kage will allow the leader to choose the name and orders.) The squad's leader will then draft members. Members are automatically put into the squad if a leader recruits them, and can then resign from the squad if they so choose. If you do not want to be accidentally brought into a squad, change your preferences to not allow an ANBU.
ANBU squads status are viewable through the town hall. Defensive points from an ANBU are received while the squad member is in the village, while Offensive Points are earned while the members is out of the village.
ANBU Members and Captains gain a damage boost when fighting in their home territory.
Members get a boost equal to: squad_rank*(territories / 100)%
Captains get a boost equal to: squad_rank*(territories / 60)%
Note: The Kage of the village may have requirements for making or maintaining a squad.
Members and leaders of an ANBU squad receive an achievements badge in the form of an ANBU mask on their Public Profile.
Former members or leaders of an ANBU squad receive an achievements badge in the form of a broken ANBU mask on their Public Profile.