This Gospel will remind us of other Gospel stories. Firstly "This is my Son, the Chosen One," relates easily to the words at the Baptism of the Lord. They also answer the evil one's triple question: "If you are the Son of God...?" There are other occasions when Peter and James and John are singled out. Notably we remember the Garden of Gethsemane and Jesus' prayer and agony.
this miracle is a special manifestation of the divinity of Jesus. It is in the order of a special miracle, a special grace for three people. It is in the order of a private audience granted as a special favour to special individuals for reasons that we can only imagine, but we can ponder in deep meditation.
This miracle is different. It is not abut healing nor deliverance, about sickness nor health. There are no petitioners. There are no crowds. Peter and James and John are taken by Jesus and led by him to be alone. They are given a private audience and they see the glory of God shining on the face of Jesus. They witness echoes of God revealing himself as thunder and lightning and storm. They are linked with the great figures of the Old Testament like Moses and Elijah. They hear the voice of the Father anointing Jesus as Son, the Beloved - listen to him. No wonder they kept silent.
We know from the second letter of Peter that the apostles remembered this encounter all their lives. (2 Peter 1:18) "We beheld the splendour of God shining on the face of Jesus."
We all have religious experience of one kind or another. I believe this Gospel is meant to encourage us to remember and share our experience of the glory of God. It is a special grace given or a future need. It is one thing to be in awe of the glory, it is another to tackle the day to day effort of living. I believe Peter and James and John were given special graces to help them in future difficulties. We remember again the teaching of Jesus that his gifts are not prizes for our virtue, but presents from his love.