What is "papal supremacy"

n. the supreme and universal power of the Pope, which he can always exercise unhindered, over the Roman Catholic Church

Papal supremacy is the doctrine of the Roman Catholic Church that the pope, by reason of his office as Vicar of Christ and as pastor of the entire Christian Church, has full, supreme, and universal power over the whole Church, a power which he can always exercise unhindered: that, in brief, "the Pope enjoys, by divine institution, supreme, full, immediate, and universal power in the care of souls."

The doctrine had the most significance in the relationship between the church and the temporal state, in matters such as ecclesiastic privileges, the actions of monarchs and even successions.