From The Gospel of John, by Francis Martin and William Wright, commenting on John 21-15-19:
This exchange between Jesus and Peter provides much food for thought about the ministry of the pope and basic aspects of the Christian life, such as sin, repentance, and discipleship. When Peter denied Jesus three times, he rejected his relationship with Jesus. In this scene, which recalls Peter’s denials, we see the tremendous love and mercy of Jesus for Peter. Jesus makes the first move and initiates the conversation with Peter. He invites Peter to repent and return to him by professing his love. With Peter’s threefold profession of love, his threefold denial is undone, and Jesus restores the relationship between them. Jesus’ mercy is so complete that he does not hold Peter’s past sins against him. Instead, Jesus gives Peter the honor and responsibility of serving as the delegated shepherd of his sheep.
The same dynamics of repentance and forgiveness apply to all disciples, for Peter is still a sheep in relation to Jesus. No matter how serious or how many the sins we have committed (Peter’s were very serious), the love and mercy of Jesus is infinitely greater. He seeks us out and invites us to return to him. This scene should give us confidence that when we seek reconciliation with Jesus, he forgives us completely and forever. As Pope Francis has beautifully taught, God “does not tire of forgiving us if we are able to return to him with a contrite heart.”