The importance of the Papacy is it comes directly from Christ's commissioning of Peter to be the visible head of the church. The teaching was reaffirmed several times.
The First Vatican Council further defines Papil infallibility, which holds the Pope. He is preserved from error when teaching dogmatic matters of faith and morals.
In Jesus' message to St. Peter he says "I will give you the keys to the kingdom of heaven. Whatever you make bonds with on earth shall bond with you in heaven and whatever you lose on earth you shall lose in heaven."
A difference was the Second Vatican Council began its first teachings on the ministry of the bishops and the first Vatican Council dealt with faith and morals.
I have neither given nor received unauthorized help on this work.