Jesus' entrance into Jerusalem is recalled by the Church at the beginning of Holy Week. It is reenacted before the beginning of the Mass for Passion Sunday, so called because the Gospel proclamation for that particular day is about the Passion of Jesus. Palm fronds are used in the reenactment where olive branches would not be available. The passage about Jesus' entrance into Jerusalem is read at the doorway of the Church and is followed by the priest's entrance and procession towards the altar for the beginning of the Eucharistic celebration. In Year A, the Church reads Matthew 21:1-11 for the reenactment. Matthew's account of Jesus' entrance is not so much a report about what happened two thousand years ago, but a proclamation of the significance of Jesus' final entrance into the city that he loved and often visited (cf. the many times Jesus goes to the Temple in the Gospel of John). Matthew retells the story of Jesus' entrance in order to invite his hearers to see in Jesus the "Son of David" who chooses the way of humility and obedience and so enters his glory as the Christ (see Matthew 28:18-20)
Below is an illustration of how to my mind Matthew presents his own version of the episode of Jesus' entrance into Jerusalem which he found in Mark.
1. The bare outline (Mark 11:1-10, see a comparison of Matthew's and Mark's texts here.). Mark narrates that when Jesus "drew near" to Jerusalem he sent two disciples into a village where they are going to get a donkey which no one has sat on. Mark 11:4-6 shows that all that Jesus ordered where done just as Jesus told them. This included even people who asked them what they are going to do with the animal. The disciples bring the animal to Jesus who sat on it after garments were thrown on it. The next scene shows Jesus making his way to Jerusalem accompanied by people who cut off branches from the trees and spreading them on the road where he passed by. All the while, the people kept shouting a phrase taken from Psalm 118 "Hosanna, blessed is he who comes in the name of the Lord." The whole episode is similar to the processions of the Feast of Tabernacles to which Psalm 118 is associated. The cry "Hosanna" means "Deliver us!"; in Psalm 118, is a dramatic call to Yahweh who has once more shown Himself as "Help" and "Savior" to the ones who call upon him (Ps. 118:13-14). Jesus enters Jerusalem as King, the Son of David, but he does so not on a horse, but on a donkey. The action recalls David, humiliated by Absalom's rebellion, riding on a donkey (two donkeys were provided him, in fact, see 2 Sam. 16:1-2) as he flees for safety (cf. 2 Sam. 16), a picture of the king who "drinks by the wayside" but who will later on "raise up his head" (Psalm 110:7).
2. Matthew's account (Matthew 21:1-11). Matthew keeps the outline provided by Mark but rewrites it by adding a fulfillment passage from Zechariah 9:9 (cf. Matthew 21:4-5).
4 All this was done, that it might be fulfilled
which was spoken through the prophet, saying,
5 Tell the daughter of Zion,
Behold, your King comes to you,
Humble, and riding on a donkey,
On a colt, the foal of a donkey.”
The fulfillment passage affected the way Matthew recounts how the disciples were commanded to get tethered animals for Jesus. In Mark, there was only one, in Matthew, the disciples got two. Perhaps Matthew also had in mind the figure of David receiving the two donkeys (2 Sam. 16:1-2). Another change that Matthew effects on the narrative is his mention of a great multitude. The festive aura of Jesus' entrance is highlighted, but so is the air of revolt with the people crying out "Hosanna to the Son of David". "Hosanna" and "Son of David" being shouted has the effect of a call to an uprising.
The branches and the cry "Blessed is he who comes in the name of the Lord" recalls Psalm 118 which calls for "appointing a holy day with shady boughs" ( v. 26, "frondosis", Vulgate, DRC ). Psalm 118 is associated with the Feast of Tabernacles where olive branches are used. It is a thanksgiving for the love that God has shown his people ("His love endures forever" is repeated at the beginning and at the close of the psalm.) and celebrates "the day that the Lord has made" (v. 24) which is a king's victory day (vv. 10-13). The psalm mentions "a stone rejected by the builders which has become the cornerstone" (v. 22), perhaps indicating how by the victory, Israel -- the smallest of the nations -- has become important. The psalm also mentions the "gate of the righteous" to which the victor enters (v. 20) and as he does so, is greeted with "Blessed is he who comes in the name of the Lord" (v. 26).
The cries of "Hosanna" in this psalm are for Yahweh, but seeing that the king is Yahweh's lieutenant, the meaning of that cry is addressed to the king as well. Matthew makes this explicit when he writes "Hosanna to the Son of David" (Hosanna' la ben-David, with the Aramaic la used in the sense of "Oh!" ). Matthew thus makes "Hosanna" a revolutionary cry that would have been unsettling for those who support the status quo. Jesus, whom Matthew has presented earlier as the Son of David (see Matthew's genealogy) will later be questioned by Pilate regarding his kingdom (Matthew 27:11).
Finally, Matthew adds a short episode regarding the reaction to Jesus entering Jerusalem.
10 When he had come into Jerusalem,
all the city was stirred up, saying,
“Who is this?”
11 The multitudes said,
“This is the prophet,
Jesus, from Nazareth of Galilee.”
The multitudes' answer to the question "Who is this?" may be surprising after all the shouting about the Son of David. One would expect the answer "King of Israel" or something to that effect. But perhaps Matthew intended the surprise. The expectation of an answer that reflects knowledge of Jesus as the "Christ", the "Anointed One" is dictated by the image of the victor king entering "the gates of righteousness" (Psalm 118). There is another psalm which the early Christians would have associated with Psalm 118:19-20. This is Psalm 24, specifically verses 7-10.
7 Lift up your heads, you gates;
Be lifted up, you everlasting doors:
The King of glory will come in.
8 Who is the King of glory?
Yahweh strong and mighty,
Yahweh mighty in battle.
9 Lift up your heads, you gates;
Yes, lift them up, you everlasting doors:
The King of glory will come in.
10 Who is this King of glory?
Yahweh of Hosts,
He is the King of glory.
In this psalm Yahweh is identified as the glorious King who enters. But Jesus' entrance is not that of glory but of humility. When the multitudes answer "Jesus the prophet" to the question "Who is he?", Matthew who had earlier given the answer "the Christ, Son of the Living God" (Matthew 16:16) through Peter, now underlines the figure of Jesus as Yahweh's Servant. Jesus does not enter Jerusalem as a conquering king, but as the Servant of Yahweh who in his obedience to God will suffer much for the sake of all.