Papal Infallibility

Infallibility is often confused with impeccability.  Impeccability is the inability to sin while infallibility (according to Catholic doctrine) is the inability to make an error in matters of faith and morals.  The Pope is infallible.  However, he is only infallible in matters of faith and morals.  Outside faith and morals, the Pope can err.  This, of course, does not mean that the Pope cannot sin. The Pope can indeed sin; therefore, he attends confessions many times.  However, in matters of faith and morals, the Pope is infallible.  In other words, there are no errors in the doctrines and catechisms of the Catholic Church nor in the Code of Canon Law of the Catholic Church despite the sins of the Pope and bishops.

The doctrine of infallibility is not a new one and goes back to Early Christianity.  According to Catholic Answers on infallibility: Christ instructed the Church to preach everything he taught (Matt. 28:19-20) and promised the protection of the Holy Spirit to "guide you into all the truth" (John 16:13).  That mandate and that promise guarantee the Church will never fall away from his teachings (Matt. 16:18, 1 Tim. 3:15), even if individual Catholics might.

It is the infallible Holy Spirit who uses fallible man to teach infallibly. The Holy Bible tells us that the Holy Spirit can speak through His bishops and priests (the bold is my emphasis). 

Mark 13:11   “But when they arrest you and deliver you up, do not worry beforehand, or premeditatefn what you will speak. But whatever is given you in that hour, speak that; for it is not you who speak, but the Holy Spirit.

Catholic Answers gives a more thorough explanation on infallibility in their website: 

Papal Infallibility

There are only two doctrines that the Pope has spoken in ex cathedra (from the chair of Peter); therefore, these two are declared "infallible."  The first to be declared in ex cathedra was the Immaculate Conception by Pope Pius IX in 1854.  The second was the Assumption of the Blessed Virgin Mary by Pope Pius XII in 1950.