At the Transfiguration, Moses was there representing the law and Elijah was there representing the prophets. But why were Peter, James, and John present? And what does this event mean to us today?
St. Thomas Aquinas devotes an entire section in his Summa theologiae to this event. His treatment sums up much of the wisdom of the Fathers, so looking at his reflections may give us some answers.
Aquinas says that it was fitting that Christ be manifested in his glory because those who are walking an arduous path need a clear sense of the goal of their journey. The arduous path is this life, with all of its attendant sufferings, failures, setbacks, disappointments, and injustices, and its goal is heavenly glory, fullness of life with God, the transformation of our bodies.
As he makes his way toward the cross, Jesus accordingly allows, for a brief time, his glory to shine through, the radiance of his divinity to appear. We are not meant finally for this world. This event is meant to awaken our sense of wonder at the world to come.
Next, Aquinas asks about the "light" or the "glory" that envelops Christ during the Transfiguration. It "shines." Why have people, trans-historically and trans-culturally, associated holiness with light? Well, light is that by which we see, that which illumines and clarifies. But at bottom it is the fact that light is beautiful. Beautiful things shine. Aquinas says that Jesus, at the Transfiguration, began to shine with the radiance of heaven so as to entrance us with the prospect of our own transfiguration.
Finally, Aquinas talks about the witnesses to the Transfiguration, namely Peter, James, John, Moses, and Elijah. Moses stands for the Law. Jesus recapitulates, perfects, and illumines the Mosaic law: "I have come not to abolish the law but to fulfill it." Christ is the new Moses, the new Lawgiver.
Similarly, Elijah stands for the prophets; he was the greatest of the prophets. The prophets spoke the words of God; Jesus is the Word of God. Therefore, the prophetic books are read in his light.
But why is Peter there? Because, says Aquinas, he loved the Lord the most. Why is John there? Because the Lord loved him the most. Why is James there? Because he was the first of the Apostles to die for his faith.
Who gets access to the glory of Jesus? Those who are tied to him through love.