On this occasion, Jesus asks Peter three times, "Do you love me?" I believe this is because he wants Peter to think deeply about the question. This is not a throw-away question. Jesus wants to offer Peter the opportunity to consider the question from different three different angles.
Certainly by the third time Jesus asks the question Peter catches on: this is not a throw away question. He needs to consider whether he loves Jesus and what that means.
So do we. Do we love Jesus? What is his word to us who say, "Yes"? I think it's the same as to Peter, "Follow me."