Immanuel is a Hebrew name that means, quite simply, God with us — from immanu (with us) and El (God). Isaiah gave it as a sign to a fearful king seven centuries before Christ: behold, a virgin shall conceive, and bear a son, and shall call his name Immanuel. It was a promise that God had not abandoned his people.
Matthew declares the promise fulfilled in the birth of Jesus: they shall call his name Emmanuel, which being interpreted is, God with us. This is the heart of the incarnation — not a distant deity, but God himself entering the world, sharing our flesh, walking our roads. And the name bookends the gospel: Jesus' final promise is lo, I am with you alway, even unto the end of the world.
Immanuel in Scripture
Therefore the Lord himself shall give you a sign; Behold, a virgin shall conceive, and bear a son, and shall call his name Immanuel.