If you attend daily Mass (a very good idea, if you can find a way to), you may have noticed the change of scenes between yesterday's Gospel and today's. Yesterday, we were in the Cenacle, on Holy Thursday, listening in on the last words of Jesus' solemn "priestly prayer" (the part in which he looked into the future and prayed specifically for us!). Today's Gospel is set after the Resurrection, on the shores of Lake Tiberias. The famous "Simon, do you love me?" passage. On this, the next-to-last day of the Easter Season, the Church wants us to hear those words, that commission: "Follow me."
We haven't heard that call (that command, really) since Chapter 1 of John's Gospel--when Jesus "finds Philip and says to him, 'Follow me'." So John is making a kind of sandwich: the call, "Follow me," is the bread that holds the filling of the Gospel together. Nothing of our faith makes sense without that "me." We just turn religion into another form of idolatry if it's not centered on Jesus. That's why Our Lord insisted on asking Peter those three times, "Do you love me?" (At the same time, the presence of the charcoal fire--a detail John also noted at Peter's denial of Christ--tells us that Jesus is giving Peter a way to come back to him, to "get behind" him, so that he would be in a position to really follow him.)