Joh 7:25 - 27 "Some of the people of Jerusalem therefore said, "Is not this the man whom they seek to kill? And here he is, speaking openly, and they say nothing to him! Can it be that the authorities really know that this is the Christ?  But we know where this man comes from, and when the Christ appears, no one will know where he comes from." 

When the people heard Jesus they recognized that He had the authority and presence of God. They saw Him   take on the religious leaders and outmatch them even though they knew He was the carpenters son. He grew up poor without opportunity to be educated but He knew and understood everything better than the religious elite. Even though they all recognized that He was the Messiah they could not give up their authority, power and pride. 
So Jesus was there teaching in the house of God. He clearly taught them that even though He grew up as a boy in Nazareth, He was sent by God The Father. He said He was from God and came from God. He was Yahweh. 
They were furious, and they wanted to kill Him, but they couldn't. He was in charge of giving and taking away life. 

Joh 7:28 - 30  "So Jesus proclaimed, as he taught in the temple, "You know me, and you know where I come from? But I have not come of my own accord. He who sent me is true, and him you do not know. I know him, for I come from him, and he sent me." So they were seeking to arrest him, but no one laid a hand on him, because his hour had not yet come." 

Even though the religious elite were against Him, many of the people believed in Him. They knew that the Messiah would act like Jesus and do the things Jesus was doing. When the religious leaders got wind of the thoughts that the crowd had they sent authorities to try to arrest Jesus. They were more afraid of losing their power than looking at who Jesus was and what His coming meant to them. 

Joh 7:31, 32  "Yet many of the people believed in him. They said, "When the Christ appears, will he do more signs than this man has done?" The Pharisees heard the crowd muttering these things about him, and the chief priests and Pharisees sent officers to arrest him." 

So Jesus told them, they would only have the gift of His presence for a little while. He was going back to heaven, to the Father and they didn't have the ability to get to heaven. 
They only thought about this world and they couldn't understand His message about heaven. Their spiritual senses were crippled. They thought He was going to go to the people of God who were outside of Judea. 

Joh 7:33-36 "Jesus then said, "I will be with you a little longer, and then I am going to him who sent me. You will seek me and you will not find me. Where I am you cannot come." The Jews said to one another, "Where does this man intend to go that we will not find him? Does he intend to go to the Dispersion among the Greeks and teach the Greeks? What does he mean by saying, 'You will seek me and you will not find me,' and, 'Where I am you cannot come'?" 

So at the end of the celebration Jesus made a final appeal to their thirsty souls. He knew they were looking for answers, for fulfillment. He said you've got to believe in Me and come to me for fulfillment. If you do come to Me for fulfillment full life will overflow from me into and through you. 
Jesus was talking about after He left He would pour out God's Spirit on those who believe. 
The people were divided some were sure He was the Messiah others couldn't get past their senses of the here and now to see to the eternal and spiritual reality. 
Some wanted Him arrested, they saw Him as crazy or a threat, but they were kept from laying a hand on Him. 

Joh 7:37 - 44 "On the last day of the feast, the great day, Jesus stood up and cried out, "If anyone thirsts, let him come to me and drink. Whoever believes in me, as the Scripture has said, 'Out of his heart will flow rivers of living water.'" Now this he said about the Spirit, whom those who believed in him were to receive, for as yet the Spirit had not been given, because Jesus was not yet glorified. When they heard these words, some of the people said, "This really is the Prophet." Others said, "This is the Christ." But some said, "Is the Christ to come from Galilee?  Has not the Scripture said that the Christ comes from the offspring of David, and comes from Bethlehem, the village where David was?"  So there was a division among the people over him.  Some of them wanted to arrest him, but no one laid hands on him."