Really the transfiguration in Luke is a Season Finale for chapter 9, it is summing up all that has taken place in Luke 9. We see that Jesus asked the Disciples "who the crowds says he is?" There response was Elijah, or a prophet of old that had risen. In v20 we see that Peter responds with he is the "Christ of God". The transfiguration takes place proving that he is not Elijah, because Elijah is there in his presence. He is also not a prophet of old because Moses is present. We also see the confirmation of Peter's proclamation by God's appearance claiming "this is my son, my Chosen one; listen to him!" To truly understand the transfiguration you must first read all of chapter 9 seeing the nuggets that help you understand why this takes place. To show the people that he is the fulfillment of the prophets along with the law of Moses.

Luke 9:28-36