The First Vatican Council was held between 1869 and 1870. This was a meeting of the pope and the bishops. The period of Church suppression during and after the French Revolution had just ended, and anti-clerical sentiments were on the rise in several other countries.
The council sought to achieve a proper balance between intellect (reason) and faith, arguing that both are necessary to correctly understand the message of Jesus. The infallibility of certain statements of the pope was decreed. Jesus gave Peter the authority to lead the early Church and to have the last word in conflicts. The pope also has this authority because he is the successor of St. Peter and is led by the Holy Spirit.