Teaching - Sanctifying - Governing
From the Catechism of the Catholic Church, Simplified
Infallibility in Faith and Morals (888-890)
As teachers of the apostolic faith, bishops must "preach the Gospel to all.".
To preserve the purity of apostolic faith, Christ gave the Church a share in his own infallibility. By their "supernatural sense of faith," the People of God (guided by the Church's Magisterium) unfailingly adhere to this faith (Second Vatican Council).
The Church's Magisterium keeps God's people from deviating from truth and guarantees professing the true faith without error. In this way, the faithful can abide in the truth because Christ endowed the Church's shepherds with the charism of infallibility in faith and morals.
Pope and Bishops (891)
The Pope is infallible when, as supreme pastor and teacher of the faith, he proclaims by a definitive act a doctrine pertaining to faith and morals.
This infallibility is also present in the body of bishops when, together with the Pope, they exercise the supreme Magisterium, above all in an Ecumenical Council. When the Church proposes a doctrine as Christ's teaching "for belief as being divinely revealed," the faithful must adhere by "the obedience of faith." This infallibility extends to the entire deposit of divine revelation.
Non-Infallible Definitions (892)
Sometimes the Pope and/or the bishops do not give an infallible definition or pronounce in "a definitive manner." Instead, by the ordinary Magisterium, they propose a teaching which leads to a better understanding of faith or morals. In these cases, the faithful must give "religious assent" to these teachings.
Sanctifying the Church (893)
The bishop (with his priests) sanctifies the Church especially through the Eucharist and by their ministry of Word, their ministry of sacraments, and by their good example.
The Bishop and His Diocese (894-896)
The bishops, as vicars of Christ, govern their dioceses by exhortations, example, and by their authority and sacred power.
In his diocese the bishop has proper, ordinary, and immediate authority which he exercises as the Vicar of Christ (although its exercise is ultimately controlled by the Church's supreme authority). Although not a vicar of the Pope, the bishop must be in union with the Pope, whose universal authority confirms the bishop's authority.
The bishop must have compassion on the ignorant and erring. He must listen to his people, who should be one with their bishop. "Let all follow the bishop as Jesus Christ follows his Father" (St. Ignatius of Antioch).