Papal infallibility is a dogma of the Catholic Church which states that, in virtue of the promise of Jesus to Peter, the Pope is preserved from the possibility of error "when, in the exercise of his office as shepherd and teacher of all Christians, in virtue of his supreme apostolic authority, he defines a doctrine concerning faith or morals to be held by the whole Church".
This doctrine was defined dogmatically in the First Vatican Council of 1869-1870. According to Catholic theology, there are several concepts important to the understanding of infallible, divine revelation: Sacred Scripture, Sacred Tradition, and the Sacred Magisterium. The infallible teachings of the Pope are part of the Sacred Magisterium, which also consists of ecumenical councils and the "ordinary and universal magisterium". In Catholic theology, papal infallibility is one of the channels of the infallibility of the Church. The infallible teachings of the Pope must be based on, or at least not contradict, Sacred Tradition or Sacred Scripture.
The doctrine of infallibility relies on one of the cornerstones of Catholic dogma: that of petrine supremacy of the pope, and his authority to be the ruling agent in deciding what will be accepted as formal beliefs in the Roman Catholic Church. The clearest example (though not the only one) of the use of this power, referred to as speaking ex cathedra expressed since the solemn declaration of papal infallibility by Vatican I on July 18, 1870, took place in 1950 when Pope Pius XII defined the Assumption of Mary as being an article of faith for Roman Catholics. This authority is considered by Catholics to be apostolic and of divine origin. Prior to the solemn definition of 1870, Pope Boniface VIII in the Bull Unam Sanctam of 1302, Pope Eugene IV in the Bull Cantate Domino of 1441, and Pope Pius IX in the Papal constitution Ineffabilis Deus of 1854 have all spoken "ex cathedra".
Read more about Papal Infallibility: Conditions For Teachings Being Declared Infallible, Ex Cathedra, Scripture and Primacy of Peter, Primacy of The Roman Pontiff, Theological History, Instances of Infallible Declarations, Denial By Catholics, Objections, Claim That Vatican I Was To Dogmatize Papal Temporal Power