The three major seasonal holy days of the Jewish calendar are Passover, Shavuot, and Sukkot. Each of these has a corresponding feast on the Christian calendar. The links between Passover and Holy Week are well-known and obvious. It's less known, but still recognized, that the Christian counterpart of Shavuot is Pentecost. What is even less known, and only very rarely recognized at all (due in part to chronological detachment), is that Sukkot, which is often known in English as the Feast of Tabernacles, also has its Christian counterpart, and the closest counterpart of Tabernacles is Transfiguration. While the Bible does not explicitly associate the Transfiguration with the Feast of Tabernacles (it is explicitly mentioned in the Gospels, if I am not mistaken, only in John 7, in a different context), but Jesus seems to have at least fairly regularly gone to Jerusalem for the major pilgrimage feasts (Passover, Shavuot, and Sukkot, again), and Peter's mention of booths or tabernacles or tents is a pretty clear indicator that the feast was going on at that time, especially given the way it is linked with the story of Peter's confession six days earlier. Sukkot is a memorial feast commemorating the wanderings of the Israelites in the desert; it is very much a thanksgiving feast, being also associated with the fall harvest. It is a big celebration, seven days long, and a sharp change from the previous major holiday, Yom Kippur. Water libations on the altar were a notable part of the celebration; when Jesus talks about water in John 7, he isn't bringing up the subject randomly -- the feast was, among other things, quite literally the feast of the waters of salvation (Isaiah 12 was, and still is, associated with the festival).
Thus we begin to get a sense of the background of Peter's thought in the story:
Jesus took with him Peter and James and John and led them up a high mountain where they could be alone by themselves. There in their presence he was transfigured: his clothes became dazzlingly white, whiter than any earthly bleacher could make them. Elijah appeared to them with Moses; and they were talking with Jesus. Then Peter spoke to Jesus: "Rabbi," he said "it is wonderful for us to be here; so let us make three tents, one for you, one for Moses and one for Elijah." He did not know what to say; they were so frightened.
And a cloud came, covering them in shadow; and there came a voice from the cloud, "This is my Son, the Beloved. Listen to him." Then suddenly, when they looked round, they saw no one with them any more but only Jesus.
As they came down from the mountain he warned them to tell no one what they had seen, until after the Son of Man had risen from the dead. They observed the warning faithfully, though among themselves they discussed what "rising from the dead" could mean.
Every single sentence of this story is striking. But we have past (Moses, Elijah) and present and future (looking forward to the Resurrection) here; we have Heaven meeting earth; we have hidden mystery and unveiling of hidden mystery simultaneously. And we have the Kingdom of God. From a sermon by St. Gregory Palamas on Matthew's version of the story:
The first thing we should consider in this Gospel passage is from what point in time Matthew, Christ's apostle and evangelist, counts the six days preceding the day on which the Lord was transfigured. Six days after which day? Six days after the day when the Lord taught His disciples, saying, "The Son of man shall come in the glory of his Father" (Mattt. 16:27), and adding, "There be some standing here, which shall not taste of death, till they see the Son of man coming in his kingdom" (Matt. 16:28). He was referring to the light of His transfiguration as His Father's glory and as His own Kingdom. (p. 267)
This is both present and hidden:
According to the theologians, when Christ was transfigured He neither received anythign different, nor was changed into anythign different, but was revealed to His disciples as He was, opening their eyes and giving sight to the blind. (p. 272)
And yet it looks forward as well. As St. Thomas Aquinas says (ST 3.45.4 ad 2):
Just as in the Baptism, where the mystery of the first regeneration was proclaimed, the operation of the whole Trinity was made manifest, because the Son Incarnate was there, the Holy Ghost appeared under the form of a dove, and the Father made Himself known in the voice; so also in the transfiguration, which is the mystery of the second regeneration, the whole Trinity appears--the Father in the voice, the Son in the man, the Holy Ghost in the bright cloud; for just as in baptism He confers innocence, signified by the simplicity of the dove, so in the resurrection will He give His elect the clarity of glory and refreshment from all sorts of evil, which are signified by the bright cloud.
I like the phrases here: the mystery of the second regeneration (sacramentum secundae regenerationis), refreshment from all sorts of evil (refrigerium ab omni malo).
One could go on forever talking about it; that is what it is to be a holy mystery: a holy mystery is an inexhaustible truth.
Quotations from Palamas are from St. Gregory Palamas, The Homilies, Mount Thabor Publishing (Waymart, PA: 2009).