When explaining the papacy to Protestant friends, I usually employ the term “steward” and use Denethor from Tolkien’s The Lord of the Rings as an example of what that means.
Denethor was the steward of the King. Denethor was not the King, did not sit on the King’s throne, but he served as the representative of the King, caring for the King’s people and realm. Now then, Denethor failed in his duties, being seduced by evil, but that fact did not revoke his stewardship, it simply made him a bad steward.
But it is not just the bishop of Rome who is the steward of God. All bishops are. St. Paul says to his disciple Titus, bishop of Crete:
For a bishop must be without crime, as the steward of God: not proud, not subject to anger, not given to wine, no striker, not greedy of filthy lucre. (Titus 1:7)
(All translations say something very similar, though they may translate bishop as “overseer” or “elder.”)
The bishop is the steward of God. Yet this immediately makes one wonder, “who can legitimately be called a bishop?” T.D. Jakes calls himself a bishop. The Protestant church down the street from us calls their preacher a bishop. Countless other Protestant preachers do as well.
If Protestantism were true, anyone who claims they are teaching the true interpretation of the Bible can say they are a bishop. All they need is a small (or large) following and suddenly people call them “bishop.” Yet every Protestant preacher thinks and claims that he is teaching the truth from the Bible.
Every heretic through all time also thought they were teaching what was true. Heretics from of old would cite Bible passages allegedly supporting their (false) teachings. Most had followers, sometimes thousands and thousands of them, who were convinced that the heretical leaders were interpreting the Bible correctly.
If Protestantism were true, all we can do is pray and read the Bible and come up with what we think is true from it and then choose those Protestant churches that most closely conform with our interpretation of Scripture.
But because Catholicism is true, we can know who the bishops really are. They are the men, like St. Titus and St. Timothy, who stand in the unbroken line of the laying on of hands from the Apostles themselves. This is Apostolic Succession through the sacrament of Holy Orders.
God made sure that His Church was not be splintered into a thousand pieces. He made sure the Church would have rightful authority, not innumerable competing men claiming authority against all the others. He made sure that bishops could be truly called His stewards, and He gave all people a sure, easy way of knowing who the bishops were.