What does Matthew 21:5 mean?
Matthew is referencing two Old Testament scriptures which carry similar messages. The first line comes from Isaiah 62:11 with the rest coming from Zechariah 9:9. He is showing how Jesus' entrance into Jerusalem on the donkey and colt are a fulfilment of these prophecies (Matthew 21:1–4). Both verses are directed at the "daughter of Zion," which was a common Old Testament name for the city of Jerusalem (2 Samuel 5:7; 1 King 8:1).The main prophetic aspect is that Zechariah describes the promised King coming to the people of Jerusalem in humility and sitting on a donkey. Zechariah specifies that the animal is a colt, the young foal of donkey or "beast of burden." Jesus will enter Jerusalem riding on the colt, likely with the full-grown donkey along for the comfort of the young one. Zechariah is describing the arrival of the King of the Jews.
The choice of a donkey is, itself, an important symbol. While the people seem to expect Messiah to be a warlike conqueror, that is not yet Jesus' mission (John 18:36). Horses are the ideal animals for war, so victorious warriors would present themselves atop a horse as they paraded. In the modern world, this would be equivalent to a general entering a conquered city on the back of a tank. Jesus, on the other hand, comes on the equivalent of a pickup truck: a workmanlike donkey. Rather than emphasizing His power, Jesus first comes in humility. His second coming, in contrast, will be one of spectacular might and judgment (Revelation 19:11–16).
Matthew doesn't quote Zechariah's middle lines that the king is coming "righteous and having salvation," but that is exactly what Jesus is doing. These words from Zechariah clearly point forward to the arrival of the Messiah in Jerusalem. Jesus has chosen that imagery to make it perfectly clear to those who know the Scriptures that He is that king.
This fulfillment, as with so many others, will serve to reinforce the faith of the disciples after Jesus' death and resurrection (John 2:22; 14:26).