Matthew writes for readers steeped in Israel's Scriptures and repeatedly explains events in Jesus' life as fulfillment. The Emmanuel citation is therefore not decorative; it supplies a theological interpretation of the child's identity and mission.
In biblical thought, God's presence with his people is a covenant blessing of enormous importance. Tabernacle, Temple, prophetic promises, and restoration hopes all revolve around the reality that God dwells with and accompanies his people.
Matthew cites Isaiah 7:14. In Isaiah's historical setting the Emmanuel sign assured the house of David that God's purposes would stand despite political crisis. Matthew sees the prophecy reaching a fuller realization in the virginal conception and birth of Jesus.
The wider biblical theme is God's promised presence: 'I will be with you' accompanies divine calling and deliverance throughout the Old Testament. Matthew develops this presence theme from the opening chapter to the risen Jesus' final promise.
Matthew explicitly translates Emmanuel for his readers as 'God with us.' The evangelist thereby places the identity of the child within the category of God's presence with his people.
The Gospel later gives this opening designation narrative depth. Jesus promises to be present where his people gather in his name, and the risen Jesus promises to be with his disciples every day until the end of the age. The beginning and ending of Matthew therefore interpret one another.
The expression should not be isolated from the rest of Matthew and made to carry every later Christian formulation by itself. Nevertheless, Matthew deliberately applies 'God with us' to Jesus and then portrays Jesus himself as the continuing presence promised to his people.
Within Matthew's complete narrative, Emmanuel becomes a strong component of divine-identity Christology: the saving presence of Israel's God is encountered in the person of Jesus.