Why did Jesus go to Jerusalem on Palm Sunday?

The Catechism of the Catholic Church (paragraphs 559-560) explains the following:

How will Jerusalem welcome her Messiah? Although Jesus had always refused popular attempts to make him king, he chooses the time and prepares the details for his messianic entry into the city of “his father David.” Acclaimed as son of David, as the one who brings salvation (Hosanna means “Save!” or “Give salvation!”), the “King of glory” enters his City “riding on an ass.” Jesus conquers the Daughter of Zion, a figure of his Church, neither by ruse nor by violence, but by the humility that bears witness to the truth. And so the subjects of his kingdom on that day are children and God's poor, who acclaim him as had the angels when they announced him to the shepherds. Their acclamation, “Blessed be he who comes in the name of the Lord,” is taken up by the Church in the “Sanctus” of the Eucharistic liturgy that introduces the memorial of the Lord’s Passover.
Jesus' entry into Jerusalem manifested the coming of the kingdom that the King-Messiah was going to accomplish by the Passover of his Death and Resurrection. It is with the celebration of that entry on Palm Sunday that the Church’s liturgy solemnly opens Holy Week.

What does Palm Sunday symbolize?

The Catechism of the Catholic Church (paragraph 570) tells us:

Jesus’ entry into Jerusalem manifests the coming of the kingdom that the Messiah-King, welcomed into his city by children and the humble of heart, is going to accomplish by the Passover of his Death and Resurrection.