One, while Elijah and Moses are representatives of God's prophets and law, respectively, they also form another specific club with Jesus. No one has relics for any of the three. Moses's grave is in an unknown location, Elijah was taken to heaven on a fiery chariot, and Jesus ascended. As humans, we build stronger connections with those things that we can touch, yet none of these men have left any such reassurance for us.
Two, Jesus is transfigured into a brilliant and beautiful form, almost to the point that his best friends cannot recognise him. This transformation is what so many people who come to Christ are seeking: to be transformed from our mundane existence. We know that we are more than our outward appearance, more than what people around us have witnessed. We long to show others our purest selves, but only after some of our baser impulses have been somehow changed into something greater, something holy.
And three, Peter suggests that he build tents for the three men with no consideration for how practical or fitting such an idea might be. We, too, rush and stumble forward in our excitement to do God's will. Occasionally, this means making missteps, sometimes ones that embarrassingly foolish. God loves us despite our failings. If He could not only forgive Peter for such recklessness, but make Peter the foundation of the Church, then there is hope for us as well.
A side note: Today was Connor's first Reconciliation. He was nervous at first, but seemed to have a good experience. The event had several stations that included the parents in the ceremony, reminding the children of the elements of their baptism. It was a nice experience.