Palm Sunday is the Sunday before Easter and the first day of Holy Week. It commemorates the day that Jesus rode into Jerusalem at the beginning of the last week of his life.
He sent some of his disciples ahead to borrow a donkey, which he said they would find tethered just outside the city, and this is the animal he rode into Jerusalem on. His choice of a donkey was a symbol that you came in peace. Riding a horse would have been a symbol of warfare.
As he entered the City, People lined the streets waving palm leaves and laying down in front of him. Christians Mark this day with a church service, sometimes including a walk through the streets carrying palm leaves.