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.)
IMPECCABILITY
(Latin: in, not; peccare, to sin)
The impossibility of sinning. Christ's human will was impeccable because of its personal union with a Divine Person. A Divine Person cannot from its very nature possess the faculty of committing sin. Concupiscence and actual sin flow from original sin which we contract by reason of our carnal descent from Adam, but Christ was conceived miraculously through the operation of the Holy Ghost. Christ Himself said: "Which of you shall convince me of sin?" (John 8). This word is often confused with infallibility. Impeccability has to do with the will and with sin; infallibility, with the intellect and with opinion or doctrine. The pope is infallible, but not impeccable.
Very good to point out the difference between those words. People get them mixed up.