This is the Sunday that begins the 'HOLY WEEK' of the Church. The feast marks Jesus' triumphant entry into Jerusalem.
Palm Sunday is usually marked by the use of palm fronds(sometimes tied to the shape of a cross) together with 'Hosanna in the highest' chants by the congregation while the do a PUBLIC procession on the streets in a similar manner like 'Christ the King'.
The symbolism is captured in Zechariah 9:9 "The Coming of Zion's King – See, your king comes to you, righteous and victorious, lowly and riding on a donkey, on a colt, the foal of a donkey". According to the Gospels, Jesus rode a donkey into Jerusalem, and the celebrating people there lay down their cloaks in front of him, and also lay down small branches of trees. The people sang part of Psalm 118: 25– 26 – ... Blessed is He who comes in the name of the Lord. We bless you from the house of the Lord ...
The symbolism of the donkey may refer to the Eastern tradition that it is an animal of peace, unlike the horse, which is the animal of war. A king came riding upon a horse when he was bent on war and rode upon a donkey when he wanted to point out he was coming in peace. Jesus' entry to Jerusalem would thus symbolize his entry as the Prince of Peace, not as a war-waging king.