What does a diocesan bishop do?

Answer 1

In the Catholic Church a Diocesan Bishop confirms, ordains Priests, administers a diocese, preaches the Holy Gospel, performs visitations of monasteries, convents, and seminaries, instructs the faithful in sound doctrine, and performs other Priestly duties as well.

An auxiliary Bishop of a diocese does whatever work he is instructed to do by his diocesan ordinary (the Bishop of the Diocese).

Bishops directly in the service of the Holy See serve in the offices of the Roman Curia, oversee certain Apostolic works, or can be employed in diplomatic service, such as Nuncios of the Holy See to various countries.

Answer 2

Catholic Answer

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The Bishop is the successor to the Apostles, and has received the fullness of Christ's priesthood. The priests under him, receive their priesthood from him and are his helpers. The Bishops are charged with being heralds of the faith, and preserving the purity of the faith handed on by the apostles. They also enjoy infallibility as a body of Bishops when they are teaching in union with Peter's successor - the Roman Pontiff.

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from Modern Catholic Dictionary by John A. Hardon, S.J. Doubleday & Co., Inc. Garden City, NY 1980

A successor of the Apostles who has received the fullness of Christ's priesthood. His most distinctive power, that of ordaining priests and other bishops, belongs uniquely to a bishop. Moreover, In spite of some disputed cases in history, it is highly probably that a priest would not be authorized by the Holy See to ordain another priest. A priest certainly cannot consecrate a bishop.

In the ordination of a bishop the "matter" is the imposition of hands on the head of the bishop-elect by the consecrating bishops, or at least by the principal consecrator, which is done in silence before the consecratory prayer; the "form" consists of the words of the consecratory prayer, of which the following pertains to the essence of the order, and therefore are required for the validity of the act: "Now pour out upon this chosen one that power which flows form you, the perfect Spirit whom He gave to the apostles, who established the Church in every place as the sanctuary where your name would always be praised and gloried."

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from The Catechism of the Catholic Church, 2nd edition

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The teaching office

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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."

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The sanctifying office

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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."

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The governing office

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895 "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.