They took palm branches and went out to meet him, shouting, "Hosanna!" "Blessed is he who comes in the name of the Lord!" (John 12:12-13)
By waving palm branches and using them to cover his path as he rode into the city on a donkey, the crowd indicated that he was revered and respected on the level of royalty, and in doing so, challenged the power of the Roman empire and priests that ruled Jerusalem.
To celebrate the occasion, many Christian churches -- both Catholic and Protestant as well as the Eastern churches -- distribute palm leaves to congregation members who then carry them in a procession either inside or outside of the church. Often the palm fronds are knotted or woven into small crosses that can be kept by individuals in their homes as a reminder of the lessons of Holy Week. In areas of the world where palm leaves are not readily available, other native plants may be substituted and Palm Sunday may be alternatively referred to as Yew Sunday, Willow Sunday, or whatever else is used in that locality.
For Christians, Palm Sunday marks the beginning of the final week of Lent and the events leading up to the crucifixion of Jesus on Good Friday and his resurrection on Easter. It is also connected to the following year's liturgical calendar as the palm leaves are often returned to the church to be burned in the next year's Ash Wednesday rituals.