The next day the large crowd that had come to the feast heard that Jesus was coming to Jerusalem.  So they took branches of palm trees and went out to meet him, crying out, “Hosanna! Blessed is he who comes in the name of the Lord, even the King of Israel!”  And Jesus found a young donkey and sat on it, just as it is written,
 “Fear not, daughter of Zion;
behold, your king is coming,
sitting on a donkey's colt!”
 His disciples did not understand these things at first, but when Jesus was glorified, then they remembered that these things had been written about him and had been done to him.  The crowd that had been with him when he called Lazarus out of the tomb and raised him from the dead continued to bear witness.  The reason why the crowd went to meet him was that they heard he had done this sign.  So the Pharisees said to one another, “You see that you are gaining nothing. Look, the world has gone after him.”
The crowd is buzzing about Jesus and are welcoming him as King, waving palm branches symbolising victory and quoting Psalm 118 with imagery of deliverance, salvation and a victorious King protecting his people.
Jesus doesn't correct them, because they're not wrong. He adds to the kingly imagery by finding a donkey to deliberately fulfil Zechariah 9:9 adding peace to the imagery of victory and salvation. Jesus is the king. He will be victorious. He will bring salvation. He will bring peace.
It's just not how they expect.
They are shouting hosanna which means save us. What did they think they needed saving from? They were shouting hosanna in anticipation of a king who would get rid of the Romans - that was the thing that they thought they needed most. Jesus was more of a king than they expected. Jesus is a better king than they expected.
They weren't shouting hosanna about their sin, their rebellion against god, the state of their own hearts or their eventual death, but those were the things that Jesus came to bring salvation from. That's why the disciples didn't understand these events until after Jesus' death and resurrection. He had saved them, from something much bigger than Roman occupation. He had conquered death, he had brought peace between us and God. He is the King.