In the Transfiguration, Jesus reveals his divine glory to the apostles Peter, John, and James. His face shone like the sun and his clothes became dazzling white (Mt 17:2). Appearing with Him were Moses and Elijah, speaking with Him about his "departure" which would occur in Jerusalem (referring to his passion). Then, a bright cloud cast a shadow over them, and a voice came from the cloud saying, "This is my Son, my Chosen; listen to him!" (Lk 9:35).
Why would Jesus do such a thing? According to the Catechism, it was to show his apostles that he was in fact divine, and that his "departure" would be a voluntary act. In other words, he didn't have to die on the cross, but rather he choose to do so. The Transfiguration also reveals the Trinity: the Father in the voice, the Son in the person of Jesus, and the Holy Spirit in the bright cloud. We also learn that we too will one day have glorified bodies like the one Christ briefly revealed to his apostles.
Catechism: Transfiguration (scroll to 554-556)
Compendium: Transfiguration (scroll to 110)