We have seen that the waving of palm branches was a tradition of the Feast of Tabernacles. Psalm 118 was also recited during worship in the celebration. Some of the words from this Psalm 118 include: 25Please, Lord, please save us (Greek – Hosanna) 26Bless the one who comes in the name of the Lord.
Jesus Enters Jerusalem to the Waving of Palm Branches
John 12: 12 The next day, the news that Jesus was on the way to Jerusalem swept through the city. A large crowd of Passover visitors 13 took palm branches and went down the road to meet him. They shouted, “Praise God! Blessings on the one who comes in the name of the Lord!
Hail to the King of Israel!” 
Even though Jesus entered Jerusalem just before Passover, the people borrowed a custom from the fall Feast of Tabernacles. These people viewed Jesus as their Messiah King and thought that He had come to deliver or save them from the Romans. Unless we understand the context of the Feast of Tabernacles, we don’t understand the depth of what the people were saying by their actions.
The people knew that Messiah would raise the dead and Jesus had just raised Lazarus from the dead (John 11). This was the talk of the town. John 12: 17 Many in the crowd had seen Jesus call Lazarus from the tomb, raising him from the dead, and they were telling others about it. 18 That was the reason so many went out to meet him—because they had heard about this miraculous sign. 
When Jesus was Proclaimed as Messiah Opposition Arose
So as Jesus comes into Jerusalem the people honored Him as God in their midst. They were praising Him as the King of Israel. They saw Jesus as the fulfillment of the hope of Israel and of the world. Thus, the Pharisees were angered. John 12: 19 Then the Pharisees said to each other, “There’s nothing we can do. Look, everyone (the world) has gone after him!”
The Pharisees had opposed Jesus before, but their plans had never worked because it was not God’s time. Now it was approaching Passover. It was God’s time as Jesus would die “as the lamb that takes away the sins of the world” on Passover.
Jesus was Immanuel or God with us and was the perfect sinless lamb that God sent to pay the price for our sins. He was, as the people of Jerusalem declared, the One who would save us. Only they had not anticipated what it would take to bring salvation to the world. But God knew and had set up a calendar that foretold what Jesus would do.
Jesus would die on Passover, remove our sin during the Feast of Unleavened Bread and rise on the Feast of First Fruits. Then the Holy Spirit would come on the Feast of Pentecost. God had a plan for our salvation that was put into place over 1400 years before Jesus was born! What a God we serve.
To hear more about the waving of palm branches, listen here:
[1-4] Holy Bible, New Living Translation, copyright © 1996, 2004, 2015 by Tyndale House Foundation. Tyndale House Publishers, Inc., Carol Stream, Illinois 60188.