From the Catechism:
551 From the beginning of his public life Jesus chose certain men, twelve in number, to be with him and to participate in his mission. He gives the Twelve a share in his authority and 'sent them out to preach the kingdom of God and to heal." They remain associated for ever with Christ's kingdom, for through them he directs the Church:“As my Father appointed a kingdom for me, so do I appoint for you that you may eat and drink at my table in my kingdom, and sit on thrones judging the twelve tribes of Israel.”
77 "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…”
860 In the office of the apostles there is one aspect that cannot be transmitted: to be the chosen witnesses of the Lord's Resurrection and so the foundation stones of the Church. But their office also has a permanent aspect. Christ promised to remain with them always. The divine mission entrusted by Jesus to them "will continue to the end of time, since the Gospel they handed on is the lasting source of all life for the Church. Therefore, . . . the apostles took care to appoint successors."
861 "In order that the mission entrusted to them might be continued after their death, [the apostles] consigned, by will and testament, as it were, to their immediate collaborators the duty of completing and consolidating the work they had begun, urging them to tend to the whole flock, in which the Holy Spirit had appointed them to shepherd the Church of God. They accordingly designated such men and then made the ruling that likewise on their death other proven men should take over their ministry."
886 "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." They extend it especially to the poor, to those persecuted for the faith, as well as to missionaries who are working throughout the world.
887 Neighboring particular Churches who share the same culture form ecclesiastical provinces or larger groupings called patriarchates or regions. The bishops of these groupings can meet in synods or provincial councils. "In a like fashion, the episcopal conferences at the present time are in a position to contribute in many and fruitful ways to the concrete realization of the collegiate spirit."
888 Bishops, with priests as co-workers, have as their first task "to preach the Gospel of God to all men," in keeping with the Lord's command. They are "heralds of faith, who draw new disciples to Christ; they are authentic teachers" of the apostolic faith "endowed with the authority of Christ."
893 The bishop is "the steward of the grace of the supreme priesthood," especially in the Eucharist which he offers personally or whose offering he assures through the priests, his co-workers. The Eucharist is the center of the life of the particular Church. The bishop and priests sanctify the Church by their prayer and work, by their ministry of the word and of the sacraments. They sanctify her by their example, "not as domineering over those in your charge but being examples to the flock." Thus, "together with the flock entrusted to them, they may attain to eternal life."
894 "The bishops, as vicars and legates of Christ, govern the particular Churches assigned to them by their counsels, exhortations, and example, but over and above that also by the authority and sacred power" which indeed they ought to exercise so as to edify, in the spirit of service which is that of their Master.
895 "The power which they exercise personally in the name of Christ, is proper, ordinary, and immediate, although its exercise is ultimately controlled by the supreme authority of the Church." But the bishops should not be thought of as vicars of the Pope. His ordinary and immediate authority over the whole Church does not annul, but on the contrary confirms and defends that of the bishops. Their authority must be exercised in communion with the whole Church under the guidance of the Pope.
896 The Good Shepherd ought to be the model and "form" of the bishop's pastoral office. Conscious of his own weaknesses, "the bishop . . . can have compassion for those who are ignorant and erring. He should not refuse to listen to his subjects whose welfare he promotes as of his very own children.... The faithful ... should be closely attached to the bishop as the Church is to Jesus Christ, and as Jesus Christ is to the Father":
Let all follow the bishop, as Jesus Christ follows his Father, and the college of presbyters as the apostles; respect the deacons as you do God's law. Let no one do anything concerning the Church in separation from the bishop.
891 …The infallibility promised to the Church is…present in the body of bishops when, together with Peter's successor, they exercise the supreme Magisterium," above all in an Ecumenical Council. When the Church through its supreme Magisterium proposes a doctrine "for belief as being divinely revealed," and as the teaching of Christ, the definitions "must be adhered to with the obedience of faith." This infallibility extends as far as the deposit of divine Revelation itself.
938 The Bishops, established by the Holy Spirit, succeed the apostles. They are "the visible source and foundation of unity in their own particular Churches."