The Feast of the Transfiguration of the Lord became widespread in the West in the 11th century and was introduced into the Roman calendar in 1457 to commemorate the victory over Islam in Belgrade. Before that, the Transfiguration of the Lord was celebrated in the Syrian, Byzantine, and Coptic rites. The Transfiguration foretells the glory of the Lord as God, and His Ascension into heaven. It anticipates the glory of heaven, where we shall see God face to face. Through grace, we already share in the divine promise of eternal life.

From the Catechism of the Catholic Church, #554:
From the day Peter confessed that Jesus is the Christ, the Son of the living God, the Master "began to show his disciples that he must go to Jerusalem and suffer many things. . . and be killed, and on the third day be raised." Peter scorns this prediction, nor do the others understand it any better than he. In this context the mysterious episode of Jesus' Transfiguration takes place on a high mountain, before three witnesses chosen by himself: Peter, James and John. Jesus' face and clothes become dazzling with light, and Moses and Elijah appear, speaking "of his departure, which he was to accomplish at Jerusalem". A cloud covers him and a voice from heaven says: "This is my Son, my Chosen; listen to him!"