Palm Sunday is the final Sunday of Lent, it also marks the beginning of Holy Week. Today we commemorate the triumphant arrival of Christ in Jerusalem, days before he was crucified.
On Palm Sunday the faithful often receive palm fronds to participate in the reenactment of Christ's arrival in Jerusalem. In the Gospels, Jesus entered Jerusalem riding on a donkey, and to the lavish praise of the townspeople who threw clothes, palms or other small branches, in front of him as a sign of homage. This was a customary practice for people of great respect.
Palm branches were a widely recognized symbol of peace and victory, hence their preferred use on Palm Sunday. Riding on a donkey instead of a horse is highly symbolic, it represents the humble arrival of someone in peace, as opposed to arriving on a horse in war.
Holy Week is the most glorious week in Christianity, it is the highpoint of the liturgical year.
The three-day period from sundown on Holy Thursday to sundown on Easter Sunday, is considered the most solemn part of the liturgical year. This period is referred to as the Easter Triduum, also known as the Sacred Triduum, or Paschal Triduum.
Basically, the Paschal Triduum is one great festival recounting the last three days of Jesus' life on earth, and the events of his Passion and Resurrection, when the Lamb of God laid down his life in atonement for our sins. "Though chronologically three days, they are liturgically one day unfolding for us the unity of Christ's Paschal Mystery" (USCCB).