Answer:
There is much speculation as to this. Two of the more common answers are…
Moses and Elijah were generally accepted as the two greatest prophets of the Old Testament and would show Peter, James and John that Jesus was truly recognized as the Son of God by those the Jewish religion regarded as the major prophets of old. It also symbolized the Deliverance (Moses leading the people out of sin and bondage) and the Prophetic Promise (which Jesus was to soon fulfill).
The second thought by many id that these two will also be the ones who will come back and be witnesses during the Great Tribulation…
Revelation 11:3-12 And I will give power unto my two witnesses, and they shall prophesy a thousand two hundred and threescore days, clothed in sackcloth. These are the two olive trees, and the two candlesticks standing before the God of the earth. And if any man will hurt them, fire proceedeth out of their mouth, and devoureth their enemies: and if any man will hurt them, he must in this manner be killed. These have power to shut heaven, that it rain not in the days of their prophecy: and have power over waters to turn them to blood, and to smite the earth with all plagues, as often as they will. And when they shall have finished their testimony, the beast that ascendeth out of the bottomless pit shall make war against them, and shall overcome them, and kill them. And their dead bodies shall lie in the street of the great city, which spiritually is called Sodom and Egypt, where also our Lord was crucified. And they of the people and kindreds and tongues and nations shall see their dead bodies three days and an half, and shall not suffer their dead bodies to be put in graves. And they that dwell upon the earth shall rejoice over them, and make merry, and shall send gifts one to another; because these two prophets tormented them that dwelt on the earth. And after three days and an half the Spirit of life from God entered into them, and they stood upon their feet; and great fear fell upon them which saw them. And they heard a great voice from heaven saying unto them, Come up hither. And they ascended up to heaven in a cloud; and their enemies beheld them.
We do not know the answer for sure, but it certainly must have been a powerful site to behold…the Son of Man in all His glory and two great men of God standing beside Him. No wonder Peter didn’t want to leave. 🙂