Some people seem to have an urge to respond to something they do not understand, by speaking, however inappropriately.  That was Peter.  The glory covering Jesus and the appearance of Moses and Elijah was way outside his experience, yet he proposed a response.  Instead of closing his mouth and bowing in awe, he stood up and spoke foolishly.

We do not know the thoughts in Peter's mind, but here are some possibilities.  Perhaps he felt that he should know what to do, and as the most assertive of the three disciples with Jesus on the mountain spoke while the others stayed silent. Or the episode in Exodus 24:9-11 could have been on his mind: when Moses took Aaron, Nadab and Abihu to witness the covenant that God had made, eating together afterwards.  Maybe he was fazed by the transfiguration and wanted to find a way of being in control, or to prolong the glorious experience (he spoke as Moses and Elijah were saying farewell to Jesus).  

Whatever his thoughts, it is obvious that he felt that it was his responsibility to supply traditional hospitality to Jesus (the Messiah), Moses (the Law) and Elijah (the Prophets): yet he failed to see that he was there by God's invitation, and Peter was the guest not the host.  That was his mistake.  He was not Jesus’ ‘minder’, to arrange His programme and protect Him.  He had the same problem on the night of Jesus’ arrest (Luke 22:54-62).  Instead of being a helper, Peter was a hinderance (Matthew 16:23) because he thought he ought to be in control, rather than Jesus.  

It was not until later that the disciples understood the significance of that day (2 Peter 1:16-21).  However, like Peter, we can make similar mistakes when God graciously exposes us to His Word and His power.  The truth is that God does many things which we cannot properly understand at the time.  Like Job and his companions, God sometimes has to tell us to 'get off the stage', because we are pathetically incompetent to know what God is doing.  Rebuking Job, God said, "Who is this that obscures my plans with words without knowledge?" (Job 38:1-2).  As Psalm 46:10 says, often our best response to what God allows - is to be still and know that only God is God!