On Palm Sunday Christians celebrate the triumphal entry of Jesus Christ into Jerusalem, the week before his death and resurrection. For many Christian churches,Palm Sunday, often referred to as “Passion Sunday,” marks the beginning of Holy Week, which concludes on Easter Sunday.
The Bible reveals that when Jesus entered Jerusalem, the crowds greeted him by waving palm branches and covering his path with palm branches. Immediately following this great time of celebration in the ministry of Jesus, he begins his journey to the cross.
The biblical account of Palm Sunday can be found in Matthew 21:1-11; Mark 11:1-11; Luke 19:28-44; and John 12:12-19.
Original source: http://christianity.about.com/od/holidaytips/qt/whatispalmsunda.htm