The Biblical justification for Palm Sunday is found in the gospel accounts. Sometime during the early part of the day, Jesus travels from Bethany to Bethphage. In the village, he mounts a colt for his travel into Jerusalem, which is a fulfillment of a Biblical Messianic prophecy (Zechariah 9:9). As he travels towards the city, a large crowd of people begins to gather who cry out praises to God. They not only cut palm tree branches to place on the road in front of Christ but also place their clothes in front of the colt (Matthew 21:1 - 9, John 12:12 -15, Mark 11:1 - 10, Luke 19:29 - 38).
The celebratory use of Palms is also found in Scripture regarding the keeping of God's Feast Days known as the Feast of Tabernacles.
39. Also in the fifteenth day of the seventh month, when you have gathered in the fruit of the land, you shall keep a feast to the LORD seven days. On the first day shall be a Sabbath, and on the eighth day shall be a Sabbath.
40. And you shall take the boughs of beautiful trees for yourselves on the first day, branches of palm trees, and the boughs of thick trees, and willows of the brook. And you shall rejoice before the LORD your God seven days. (Leviticus 23:39 - 40, HBFV)
According to Adam Clarke's Commentary on the Bible, these and other branches were emblematical of victory and success.
In churches who celebrate the feast, palms, (or parts of yew, willow, or other native trees) may be distributed to worshippers on the day. They may also be burned, blessed, and their ashes kept for use for the following year's observance of Ash Wednesday.
A rather strange tradition related to the observance of this religious period occurred in England during the 15th to 17th centuries. An effigy of Judas Iscariot, made of straw or other materials and called a Jack 'o' Lent, was stoned, beaten and dragged through the streets on Ash Wednesday. It was kept until Palm Sunday (or Good Friday), where it was then burned.