This is a great gift that the Father gave a glimpse of the future glory of Christ in His risen humanity to the three disciples on the mountain. In the bible, we find that Jesus Christ went to mountain to pray. Usually He prayed alone. This time he took three of His disciples Peter, James and John. At the transfiguration Moses and Elijah came near Jesus whose face shone as the sun and his garments became a brilliant white.
This scene on the mountain was intended by Christ to be an encouragement to His disciples to remain steadfast in the terrible test of faith, which His passion and death was soon to be for them.
He understood the human weakness of the disciples. Through His transfiguration, Jesus was teaching them that after the suffering there would be great glory. When they were watching the glorious scene they wanted to stay there forever. If we want to enjoy the heavenly happiness we have to go through purification and clean our souls through our suffering.