St. Augustine of Hippo comments:
We may wonder what advantage there could be for Christ in Peter’s love for him. If Christ loves you, you profit, not Christ; and if you love him, again the advantage is yours, not his. But wishing to show us how we should demonstrate our love for him, Christ the Lord made it plain that it is by our concern for his sheep. Do you love me? he asked. I do love you. Then feed my sheep. Once, twice, and a third time the same dialogue was repeated. To the Lord’s one and only question, Peter had no other answer than I do love you. And each time the Lord gave Peter the same command: Feed my sheep. Let us love one another then, and by so doing we shall be loving Christ.
But listen to John’s words: If you do not love the brother that you can see, how can you love the God you cannot see? It is by loving the sheep that you show your love for the shepherd, for the sheep are the members of the shepherd. Indeed, it was to make the sheep members of his own body that the Lord became one of them himself, that he allowed himself to be led like a lamb to the slaughter, and that he allowed the Baptist to point him out and say to him: Behold the Lamb of God, who takes away the sins of the world. Surely a crushing burden for a lamb! But that lamb possessed tremendous strength. Do you wish to know how much strength was in this lamb? Because the lamb was crucified, the lion was overcome. If he could vanquish the devil by his own death, think with what power he is able to rule the world! May nothing, then, ever be dearer to us than Christ the Lord; let us love him with all our hearts.