The Transfiguration is the incident in the life of our Lord, recorded in all three Synoptics and recalled by Peter in his second epistle, in which Jesus took Peter and James-and-John (Sons of Thunder™) (the only apostles with superhero titles) up on a mountain where he was transfigured (changed) before them, shining with a blinding light. In the Orthodox Church this light is called “uncreated” and identified with God’s Energies; the Catholic Encyclopedia calls it “an interior shining of His Divinity.” Either way not your average 800 lumen bulb.
Suddenly, Moses and Elijah appeared with him, causing Peter to burble, “Lord, this rocks. Let’s make booths for all three of you.” (Strangely (or not), the account in 2 Peter fails to mention this detail.) A voice then boomed from heaven, “This is my son. Shut up and listen to him.” (The “shut up” is only implied, albeit very loudly.) The disciples were scared witless, and fell upon their faces (many Orthodox icons show them losing their sandals to signify their disarray) (which is delightful), but they were comforted by Christ: “Don’t be scared. But this is all strictly under wraps until after the Resurrection, dig?” When they looked again, Moses and Elijah had been transported elsewhither.
Church Fathers, theologians, doctors, historians, iconographers, and (to a lesser extent) janitors have been fascinated with the Transfiguration from the very beginning. Iranaeus (ca. 130–202) certainly was, and Thomas Aquinas called it the “greatest miracle.” Bob, seventh-century janitor at St. Catherine’s Monastery on Mt. Sinai, is someone I made up just now.
Moses and Elijah have been taken (by, inter alia, Origen and Martin Luther) to represent the Law and the Prophets, and thus the Old Testament as a whole (cf. e.g. Matt 22:40, Luke 16:16, et al.) (like the Latin?). Tradition identifies the location as Mount Tabor in present-day Israel (32°41′13.61″N 35°23′25.38″E—or, about four miles due east of Nazareth). The top of the mountain is shared by a Franciscan monastery complex (completed in 1924) and an Orthodox Church (completed in 1845 or 1862), which may incorporate bits of the twelfth-century Crusader church.
The Feast of the Transfiguration is mentioned as early as the ninth century, is one of the Twelve Great Feasts* of Orthodoxy, and was made a Universal Feast of the Church in the West by Pope Callixtus III to commemorate the Siege of Belgrade in 1456. At one time it was celebrated during Great Lent (the pericope of the Transfiguration is still read on the Second Sunday of Lent on the Roman calendar). In the Orthodox calendar, the feast falls during the Dormition Fast (August 1–14), but the fast is relaxed to allow fish, wine, and oil (a missing comma in that phrase occasionally gives rise to inquiries regarding “fish wine”—grammar matters, children). It is also the occasion of the “blessing of the grapes” (or apples in non-grape growing regions) (what they bless in places where neither apples nor grapes grow, my sources do not divulge). The Germans, Martin Luther notwithstanding, abandoned the feast after the Reformation, although many other Protestant traditions still celebrate it, some in Lent, some just before Lent, and some on August 6. Which, if you think about it (with all due respect) (or without it), is the sort of variety you’d expect in Protestantdom.
 Actually “suddenly” is not specified; they could have faded in like people in the transporter room on Star Trek for all we know. But I know which I think more likely.
 The word “booths” lends credence to the theory that this transpired during the Jewish festival of Sukkoth (“Booths”) (cf. Leviticus 23:39–43), during which families dwell (nowadays some just eat) outdoors in, well, booths.
 Mark, by tradition a companion of Peter, gives this as an excuse for the “booths” remark.