What does John 21:15 mean?

Peter, John, and five other disciples are eating with a resurrected Jesus on the shores of Galilee. Jesus has just performed a miracle, resulting in a huge catch of fish (John 21:6, 11). That echoed an earlier miracle where Jesus had first called Peter to become a disciple (Luke 5:5–11). Only a few days earlier, Peter had stood by a fire and denied even knowing Jesus (John 13:36–38; 18:25–27). Now Peter stands by another fire, and Jesus will make him repeat his loyalty three times (John 21:16–17).

Jesus' question about whether Peter loves Him "more than these" is probably a reference to the other disciples. Jesus is asking "do you really love Me more than they love Me?" That speaks to Peter's self-assured bragging shortly before Jesus was arrested (Mark 14:29). Three times, Peter denied Jesus. Three times, Jesus will make Peter confess His faith.

Greek vocabulary has more than one word for the English term "love." As in English, however, words can have nuanced and overlapping meanings. Jesus will use two root words, agapaō and phileō, in His questions. Peter will only use phileō. While these words can have separate meanings, in their own contexts, their use here is essentially identical. The same is true of Jesus' three commands, which mix terms like "feed" and "tend" with references to "sheep" and "lambs."