Matthew 21:4-5 This took place to fulfill what was spoken by the prophet, saying, (5) “Say to the daughter of Zion, ‘Behold, your king is coming to you, humble, and mounted on a donkey, and on a colt, the foal of a beast of burden.'”
As Jesus approaches Jerusalem for the last time during his earthly life, he begins to act out the fulfillment of messianic prophecy. Matthew specifies that Jesus’ entrance into Jerusalem upon a colt fulfills the prophecy of Zech. 9:9. Jesus’ action is an open declaration that he is the righteous Davidic Messiah. The first line of the OT quotation, however, is from Isa. 62:11 and uses the phrase daughter of Zion to refer to the inhabitants of Jerusalem. The prophecy really opens up when you consider the full verses that Matthew uses in their Old Testament context brought forward to the New Testament.
Matthew first quotes Isaiah 62:11
Behold, the LORD has proclaimed to the end of the earth: Say to the daughter of Zion, “Behold, your salvation comes; behold, his reward is with him, and his recompense before him.”
The first 10 verses of Isaiah 62 deal with Israel’s restoration beyond the coming captivity in Babylon. Verse 11 is explicitly Messianic: the Lord is proclaiming to the people that their savior [salvation] will come through a specific person.
Next, Matthew includes Zechariah 9:9:
Rejoice greatly, O daughter of Zion! Shout aloud, O daughter of Jerusalem! Behold, your king is coming to you; righteous and having salvation is he, humble and mounted on a donkey, on a colt, the foal of a donkey.
Notice how Zechariah likewise speaks of salvation of Israel. But this salvation bringing king is humble and on and donkey, not a man of war on a horse but a man of peace [Zech. 9:10].
A full understanding of these passages could include all the above:
Behold daughter of Zion, you salvation is coming in the form of a King that is righteous and humble bringing peace and not war and He brings His reward with him.