Palm Sunday is a reminder to welcome Jesus into our hearts, praise Him and acknowledge that He is the King of kings.
Leviticus 23:40 says,
"And you shall take for yourselves on the first day the fruit of beautiful trees, branches of palm trees, the boughs of leafy trees, and willows of the brook; and you shall rejoice before the LORD your God for seven days."
John 12:13 says,
"They took branches of palm trees, and went forth to meet Him, and cried, 'Hosanna: Blessed is the King of Israel that comes in the Name of the Lord.'"