Here is a wonderful commentary on today's gospel reading, from Saint Augustine (354-430), Bishop of Hippo (North Africa) and Doctor of the Church
from Sermon Guelferbytanus 16, 1, PLS 2, 579
"After his resurrection, the Lord appears again to his disciples. He questions the apostle Peter, obliging him to confess his love, whereas he had disavowed it three times by fear. Christ had risen according to the flesh, and Peter according to the spirit. As Christ had died while suffering, Peter died while denying. The Lord Christ had risen from the dead, and he raised Peter thanks to Peter's love for him.
He asked him questions about his love which he confessed openly now, and he entrusted his sheep to him. What did Peter bring to Christ by the fact that he loved him? If Christ loves you, it is profitable for you, not for Christ. If you love Christ, it is still profitable for you, not for him.
However the Lord Christ, wanting to show us how we must prove that we love him, us reveals how clearly: by loving his sheep. Simon, son of John, do you love me? - I love you. - Tend my sheep." And that once, twice, three times. Peter speaks only of his love. The Lord does not ask him anything else but love, and entrusts only his sheep anything else to him. Therefore, let us love one another, and we will love Christ."