Freedom from error in teaching the universal Church in matters of faith or morals. As defined by the First Vatican Council, "The Roman Pontiff, when he speaks ex cathedra—that is, when in discharge of the office of pastor and teacher of all Christians, by virtue of his supreme apostolic authority, he defines a doctrine regarding faith or morals to be held by the universal Church, by the divine assistance promised to him in Blessed Peter, is possessed of that infallibility with which the divine Redeemer willed that his Church should be endowed in defining doctrine regarding faith or morals; and therefore such definitions are irreformable of themselves, and not in virtue of consent of the Church" (Denzinger 3074).
The bearer of the infallibility is every lawful Pope as successor of Peter, the Prince of the Apostles. But the Pope alone is infallible, not others to whom he delegates a part of his teaching authority, for example, the Roman congregations.
The object of his infallibility is his teaching of faith and morals. This means especially revealed doctrine like the Incarnation. But it also includes any nonrevealed teaching that is in any way connected with revelation.
The condition of the infallibility is that the Pope speaks ex cathedra. For this is required that: 1. he have the intention of declaring something unchangeably true; and 2. he speak as shepherd and teacher of all the faithful with the full weight of his apostolic authority, and not merely as a private theologian or even merely for the people of Rome or some particular segment of the Church of God.
The source of the infallibility is the supernatural assistance of the Holy Spirit, who protects the supreme teacher of the Church from error and therefore from misleading the people of God.
As a result, the ex cathedra pronouncements of the Pope are unchangeable "of themselves," that is, not because others in the Church either first instructed the Pope or agree to what he says. (Etym. Latin in-, not + fallibilis; from fallere, to deceive: infallibilis, not able to deceive, or err.)