"Simon son of John, do you love me more than these? ..." (John 21:15)

When they had finished eating, Jesus said to Simon Peter, “Simon son of John, do you love me more than these?” “Yes, Lord,” he said, “you know that I love you.” Jesus said, “Feed my lambs.” (John 21:15)

What does 'feed my lambs' mean?

Jesus told Peter, "Feed my lambs." What does this mean?

First, the question being asked is translated somewhat oddly in the NIV. The phrase "more than these" is being taken from the Greek phrase πλέον τούτων. The word πλέον refers to "more" or "greater" and the word τούτων is a pronoun that would mean "them" or "they" or "these."

However, "these" would indicate an impersonal pronoun. As if Jesus is comparing loving himself with loving some objects that were around Peter. Really?

No. Jesus is comparing the love that Peter is theoretically showing others, including his companions, with the love that Peter has for Jesus.

Why would Jesus ask Peter this? To Peter it is more of a rhetorical question, as Peter says, "you know that I love you."

But it was not a rhetorical question for Jesus, because Jesus is seeing that his disciples have gone out fishing.

Is this what Jesus wants Simon Peter to be doing after Jesus sacrificed so much to give his teachings to others? Was this what Jesus wanted his disciples to be doing after his physical body was murdered because of his teachings? That they should go back to doing what Jesus had found them doing when he first recruited them to follow him? Fishing?

No. Jesus' first and foremost teaching was:
“‘Love the Lord your God with all your heart and with all your soul and with all your mind.' This is the first and greatest commandment." (Matt. 22:37-38)

What did Jesus want Peter to do?

Jesus didn't want Peter to return to being a fisherman. He wanted him to go out preaching love for God as he had. He wanted him to serve the Supreme Being by passing on these teachings to others.

We must ask: Why does a person fish? To feed themselves and others. A commercial fisherman like Simon and his companions were catching enough fish to feed many others along with themselves. How do we know they were able to feed many others? Because they were fishing with big nets:
So Simon Peter climbed back into the boat and dragged the net ashore. It was full of large fish... (John 21:11)
This is why Jesus is asking Peter if he loved Jesus more than he loved others. By fishing, Peter was working to feed others. Professional fisherman or otherwise, the result was the feeding of others.

And this is also the purpose of Jesus following his supposedly rhetorical question with, "Feed my lambs."

Jesus was comparing the current task of Simon Peter with the task that Jesus wants him to do. If Simon Peter loves Jesus more than he loves others, then he will work on behalf of Jesus and the Supreme Being.

In other words, he will serve his spiritual teacher and the Supreme Being by passing on the teachings of God's representative to others.

This is the task that Jesus is instructing Simon Peter to do.

Why does Jesus want Peter to love him?

Does this mean that Jesus is the Supreme Being? Certainly not. Rather, the ancient relationship between the spiritual teacher and their followers is precisely one of love. The spiritual teacher loves each follower and introduces them to the Supreme Being.

This is accomplished because the spiritual teacher enjoys a loving relationship with God. A serious student of such a teacher will become dedicated to the teacher and follow their teachings closely. This creates an exchange of love, allowing the student the opportunity to gain a personal relationship with God.

This custom was evident in the Old Testament, for example as Samuel served and honored Eli, and as Joshua served and honored Moses. It was also evident as Jesus loved and served John the Baptist, then began preaching when John was imprisoned. And it was evident as Jesus' students loved and served Jesus and began preaching on behalf of Jesus after his departure.

The fact that Jesus was instructing Peter to preach on his behalf is evidenced by the fact that Peter does, in fact, give up being a fisherman and takes up the mission of passing on Jesus' teachings to others. Peter is to become a great spiritual teacher by passing on the teachings of Jesus. Peter also takes on his own disciples.

We should note that Peter's teachings reflected Jesus' teachings, but Paul's teachings did not. Paul created a new doctrine - called the Pauline doctrine - that departed from Jesus' teachings. The Roman Catholic doctrine and most of the other Christian sects to come have also embraced the Pauline doctrine.

This is despite the fact that Peter is credited for being the first Pope.

And what did Peter teach? As Jesus taught, Peter taught that love for God and praising God's Holy Names is the path to salvation:
"And everyone who calls on the Name of the Lord will be saved." (Acts 2:21)