Palm Sunday is the final Sunday of Lent, the beginning of Holy Week, and commemorates the triumphant arrival of Christ in Jerusalem, days before he was crucified.
Palm Sunday is known as such because the faithful will receive palm fronds which they use to participate in the reenactment of Christ’s arrival in Jerusalem. In the Gospels, Jesus entered Jerusalem riding a young donkey, and to the lavish praise of the townspeople who threw clothes, or possibly palms or small branches, in front of him as a sign of homage. This was a customary practice for people of great respect.
Palm branches are widely recognized symbol of peace and victory, hence their preferred use on Palm Sunday.
The use of a donkey instead of a horse is highly symbolic, it represents the humble arrival of someone in peace, as opposed to arriving on a steed in war.