What does Matthew 21:9 mean?

Matthew paints a vivid scene. Jesus, riding on a donkey into Jerusalem (Zechariah 9:9), is followed by a great crowd that has travelled the road with Him toward the city for Passover. People already in the city have heard that Jesus is coming, and another crowd emerges to meet Him as He enters (John 12:12–13).

It's a celebration. Matthew has already described how most of the people are taking off their cloaks and putting them in Jesus' path has He rides, as well as spreading branches in the road before Him. This is an act of submission to royalty (2 Kings 9:13). Here, he explains what it sounded like as Jesus made His triumphal entry.

The crowds shout words from Psalm 118:25–26. The word "Hosanna" literally means "save," as it is used in Psalm 118, but it came to be a cry of praise for the One who had done the saving. The crowds call Jesus "the Son of David," which is a name for the promised Messiah (Matthew 1:1). They also shout, "Blessed in he who comes in the name of the Lord!" And "Hosanna in the highest!" from those verses.

Some commentators point out that it is likely these verses were regularly shouted by the people to each other during the Passover season. That may be true, but in this case the words are clearly directed at Jesus, specifically. The following verse shows that the whole city was stirred up because of Him. Some want to know who He is. Others describe Him as the prophet of Nazareth. Still others clearly believed Him to be the Messiah in this moment, though they give up that hope later in the week when Jesus is arrested and condemned instead of taking the throne of Israel and overthrowing the Romans (John 18:4–12).