For Matthew, Jesus is the long-awaited Jewish messiah whom the prophets had promised. He is the messenger that was promised in Malachi 3, who will come into the Temple and refine the religious leaders. From the opening genealogy through the final recorded words of Jesus after his resurrection, Matthew shares countless ways in which Jesus fulfills the descriptions of the messiah in the prophets. Sometimes Matthew does this explicitly, citing the prophetic writings; often, though, it is simply assumed that the reader will recognize these parallels.
You don't need to be an expert in Jewish prophecy, though, to get swept away by the story and teachings of Jesus in Matthew. Here, Jesus is a profound teacher, offering lengthy sermons about righteousness and faith. Usually, these stories upend expectations -- and the usual teaching of other Jewish religious leaders of the time. Always, they pursue a purity of spirit, rather than simply insisting on good behavior, as the true goal of faith -- which is a much higher and more difficult standard.
As people of faith, we are expected to see Jesus in Matthew as the angel describes him to Joseph -- God with us. In Matthew, Jesus is God walking through the earth, sharing God's eternal wisdom while confronting bad religious teaching. Jesus is God caring for all people -- eating with them, healing them, paying attention to them -- rather than limiting his time to people of status who "deserve" it. Jesus is God admitting that the path of faith is extremely challenging and sometimes even dangerous in this sinful world -- which is proven true by his own arrest and crucifixion. And Jesus is God proving that this world does not have the final word, resurrected to new life and promising the same to those who would follow him.