“But he told him, ‘If they don’t listen to Moses and the prophets, they will not be persuaded if someone rises from the dead.’” -Luke 16:31
Moses represents the law (the first five books of the Bible) and Elijah the prophets (the rest of the Old Testament), which both refer to God’s Word.
2 After six days Jesus took Peter, James, and John and led them up on a high mountain by themselves to be alone. He was transformed in front of them, 3 and His clothes became dazzling—extremely white as no launderer on earth could whiten them. 4 Elijah appeared to them with Moses, and they were talking with Jesus.
Jesus wanted to show some of His disciples His glory. These three disciples were going to be leaders after Jesus’ departure back to the Father.
When James, Cephas, and John, recognized as pillars, acknowledged the grace that had been given to me, they gave the right hand of fellowship to me and Barnabas, agreeing that we should go to the Gentiles and they to the circumcised. -Galatians 2:9
So, the disciples seeing Moses, Elijah, and Jesus was to show them God’s full revelation to humanity. The gospel of Luke in Chapter 9 records the discussion that Jesus had with Moses and Elijah. They were talking about the exodus, the departure of Jesus from the world. The word exodus as we know it was when Moses took the Israelites from the bondage of Egypt to the promised land. The bondage of Egypt represents the world of sin, and the promised land represents heaven. Jesus was now getting ready to die for the sins of the world so that we may have access to heaven. Anyone who puts their trust in Jesus Christ and His finished work on the cross will receive eternal life.
Moses received God’s Word from God and said that one like him was coming. Elijah represented all of the prophets. The prophet Isaiah wrote in Isaiah 53 what the Messiah was going to do for all humanity. And Jesus fulfilled those prophecies by His death on the cross and resurrection.
An update with added details from the post: Why Jesus Met With Moses And Elijah
The Scriptures were taken from the HCSB