Foundational to the Catholic Church, the Petrine Doctrine very, very basically claims that Jesus gave the apostle Peter special authority, turning him into the first pope and making him the sole custodian of the Christian faith, an authority that would continue to be passed on to his successors.
The Catholic catechism still states that the pope “as pastor of the entire Catholic Church, has full, supreme, and universal power over the whole church, a power which he can always exercise unhindered.” This is known as “papal supremacy.”
Peter probably didn’t know what he was getting himself and his successors into. Being sole custodians of the Christian faith was a huge job. There were unCatholic people everywhere that needed to be brought into the fold.
Also, the only thing that confirms this actually happened are a couple of bible verses (Matthew 16:18, for one, although of course there’s a lot of confusion given that it’s been translated through a few languages).
There are a long succession of popes after that, but for the sole purpose of staying on topic, we’ll jump a few to June 18, 1452, when Pope Nicholas V issues a papal bull called the Dum Diversas.