Palm Sunday always takes place the Sunday before Easter, during the Lenten season. It is during this Sunday we are supposed recall how Jesus rode into Jerusalem just days before his crucifixion. According to scripture, when he rode in, people threw down coats and palms before him. They yelled "Hosanna."
In many Protestant churches, we recall this time by having the children bring in the palms, and placing them at the communion table.
Palm Sunday marks the beginning of Holy Week.