Q. 1. What does the expression "Papal Infallibility" mean?
A. 1. First it is important to understand the Catholic meaning of "infallibility." According to the catholic Encyclopedia, in general, infallibility is an exemption or immunity from liability to error or failure; in particular in theological usage, the supernatural prerogative by which the Church of Christ is, by a special Divine assistance, preserved from liability to error in her definitive dogmatic teaching regarding matters of faith and morals.
On this matter, the teaching of the Catholic Church found in Canon Law is:
Can. 749 §1 In virtue of his office the Supreme Pontiff is infallible in his teaching when, as chief Shepherd and Teacher of all Christ’s faithful, with the duty of strengthening his brethren in the faith, he proclaims by definitive act a doctrine to be held concerning faith or morals.
§2 The College of Bishops also possesses infallibility in its teaching when the Bishops, gathered together in an Ecumenical Council and exercising their magisterium as teachers and judges of faith and morals, definitively declare for the universal Church a doctrine to be held concerning faith or morals; likewise, when the Bishops, dispersed throughout the world but maintaining the bond of union among themselves and with the successor of Peter, together with the same Roman Pontiff authentically teach matters of faith or morals, and are agreed that a particular teaching is definitively to be held.
§3 No doctrine is understood to be infallibly defined unless this is manifestly demonstrated.