The Catholic Catechism on Papal Infallibility
This is what the Catholic church claims:
In order to preserve the Church in the purity of the faith handed on by the apostles, Christ who is the Truth willed to confer on her a share in his own infallibility. By a “supernatural sense of faith” the People of God, under the guidance of the Church’s living Magisterium, “unfailingly adheres to this faith.”
The Roman Pontiff, head of the college of bishops, enjoys this infallibility in virtue of his office, when, as supreme pastor and teacher of all the faithful—who confirms his brethren in the faith he proclaims by a definitive act a doctrine pertaining to faith or morals. . . . The infallibility promised to the Church is also 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.
Check out the Vatican’s official site sometime. It’s good to be aware that it exists, and I have to admit I think the design is pretty cool—even though it hasn’t changed much for a long time.