Papal primacy is the concept that the bishop of Rome (the pope) is the universal pastor and supreme head of the Catholic Church.
He has full, supreme, immediate, and universal jurisdictional authority to govern the church. This means that no bishop, synod, or council of bishops can override his authority. His teaching authority is defined in the doctrine of papal infallibility. His governing authority is contained in papal primacy.
The Eastern Orthodox Church considers the bishop of Rome to have a primacy of honor among the five patriarchs of Jerusalem, Alexandria, Antioch, Constantinople, and Rome. They do not recognize his primacy of jurisdiction, however.
Every bishop in the Catholic Church must be approved by the pope and receive a papal mandate before being ordained and consecrated to the episcopacy (bishopric), and it is the pope who confers on that bishop the authority to govern the diocese to which he has been appointed.
The First Vatican Council defined papal infallibility and papal primacy. “All the faithful of Christ must believe that the Apostolic See and the Roman Pontiff hold primacy over the whole world, and that the Pontiff of Rome himself is the successor of the blessed Peter, the chief of the apostles, and is the true Vicar of Christ and head of the whole Church and faith, and teacher of all Christians.” (See also Catechism #882.)
The basis for the teachings on papal primacy and papal infallibility are found in Matthew 16:17–19 when Jesus said to Simon, “Blessed are you, Simon bar-Jonah, for flesh and blood has not revealed this to you, but my heavenly Father. And so I say to you, you are Peter, and upon this rock I will build my church, and the gates of hell shall not prevail against it. I will give you the keys to the kingdom of heaven.
Whatever you bind on earth shall be bound in heaven; and whatever you loose on earth shall be loosed in heaven.”
Some who dispute papal primacy claim that the original Greek words used by Matthew (Petros for Peter and petra for rock) show a difference between rock and stone, as if Peter were a small stone and the church was a large rock. Actually, the Greek word for stone is lithos. Petros is nothing more than petra (rock) with a masculine ending.
Calling Simon “petra” would be like calling John “Joan” or “Johanna.” A bunch of fishermen would tease him mercilessly had Jesus given him a name with a feminine ending, something our English language does not have.
So despite the feminine ending of Petra, linguistic and biblical scholarship maintains that Simon “Peter” is the rock upon which Christ built his church.