What are the tongues of fire over the head of those in the upper room in Acts 2?

Acts 2:1-4 “And when the day of Pentecost was fully come, they were all with one accord in one place. And suddenly there came a sound from heaven as of a rushing mighty wind, and it filled all the house where they were sitting. And there appeared unto them cloven tongues like as of fire, and it sat upon each of them. And they were all filled with the Holy Ghost, and began to speak with other tongues, as the Spirit gave them utterance” (KJV)

This manifestation was a reminder of what seen by Moses in the burning bush, and the priests that ministered in the Holy of Holies; above the Ark of the covenant, the shekinah glory. When the curtain of the Holy Place was torn in two when Jesus died it was a sign to the Jews that the Old Covenant was no longer the way God dwells with man. Tongues of fire (cloven tongues) in the KJV does not mean they looked like tongues. The tongues of fire was the visible sign of glory, it resembled fire in its luminosity. The Holy Spirit was sent to dwell in the NEW Temple, the body of Christ (1 Cor.3:16-17).

cloven diamerizo; to partition thoroughly (literally in distribution, figuratively in dissension):

KJV-- cloven, divide, part. In other words the glory of God was distributed, spread and seen among each person. This was a unique one time event never to be repeated in the apostles ministry or church history since (despite claims of it taking place.)

The glory, being filled with the Spirit prompted them to speak in tongues (languages they did not learn Acts 2:4) The Holy Spirit came upon them and entered into the Apostles, and the Apostles spoke in tongues to their Jewish brethren. They were baptized in the Holy Spirit (immersed). And the Body of Christ officially began with their preaching to their brethren.