"In order that the full and living Gospel might always be preserved in the Church the apostles left bishops as their successors. They gave them their own position of teaching authority."
(Catechism of the Catholic Church, 77)
"The individual bishops are the visible source and foundation of unity in their own particular Churches. As such, they exercise their pastoral office over the portion of the People of God assigned to them, assisted by priests and deacons. But, as a member of the episcopal college, each bishop shares in the concern for all the Churches. The bishops exercise this care first by ruling well their own Churches as portions of the universal Church, and so contributing to the welfare of the whole Mystical Body, which, from another point of view, is a corporate body of Churches."
(Catechism of the Catholic Church, 886)
Bishop can be:
1. Diocesan, who is entrusted the care of the people of particular diocese:
a) Resident Bishop, if he is a subject to metropolitan and his diocese is a part of some Church province,
b) Exempt Bishop, if he doesn't belong to any province and is a subject to the Holy See.
a) Coadjutor Bishop, who possesses a right of succession,
b) Auxiliary Bishop, who can or needn't have any special privileges.
3. Emeritus, if he lost his office by virtue of age or accepted resignation.