I assume from your comment that you are asking about John 21:20-24, not John 20: "Peter turned and saw following them the disciple whom Jesus loved, who had lain close to his breast at the supper and had said, 'Lord, who is it that is going to betray you?' When Peter saw him, he said to Jesus 'Lord, what about this man?' Jesus said to him 'If it is my will that he remain until I come, what is that to you? Follow me!' The saying spread abroad among the brethren that this disciple was not to die; yet Jesus did not say to him that he was not to die, but 'If it is my will that he remain until I come, what is that to you?' This is the disciple who is bearing witness to these things, and who has written these things, and we know that his testimony is true."
Historically, it's clear that this odd passage was intended to put to rest certain rumors that had become popular in the years since Jesus' earthly ministry had ended. John is the last of the Gospels to be written, in the final years of the first Christian century; so if it was indeed written by the same John who was known as the 'beloved disciple,' he would be a very old man. If it was believed that Jesus had said he wouldn't die, and then he did, in fact, die, it might confuse or dismay many people. So he takes pains to emphasize, in the final verses of the Gospel that bears his name, that Jesus never said that.
Metaphysically, Peter represents the power of Faith, and John the power of Love. Their interaction here suggests, I think, that even our most powerful and important spiritual powers can be distorted by resentment and other negative energies if we're not careful to "keep our eye single" and our focus clear. Peter seems to be distracted by a resentment of Jesus' close relationship with John. (Remember, of course, that it is John who is describing the relationship as special; Thomas claims an equally special relationship in the Gospel that bears his name.) The key sentence, which is useful any time my spiritual purpose gets distracted by human concerns, is Jesus' saying "What is that to you? Follow me!" In other words, our spiritual task is to fully express our own Christ energy, not to be concerned with how others are, or are not, expressing theirs.