For you see, it does not make sense in the English that Jesus asked Peter three times about his love, and Peter each time says yes, he does love his Lord. In the English translations it is foolish and repetitive. But in the Greek it comes alive. For the Greeks had four words for love, three of them are in our Greek New Testament. Agape, the word for the God-like love, the highest love there is.
Philia is the word for friendship, and eros is the physical or erotic kind of love.
The first time Jesus asks Simon if he loves him he uses the agape, the God-like love. The second time, Jesus uses the word agape again. And Peter again uses philia, the friendship word. And Peter affirms that such is what he has been saying. It seems that Jesus finally gets the point.