The child
Isaiah had just announced that a virgin would conceive and bear a son (Isaias 7:14). Two chapters later, he says more about who this child would be:
"For a child is born to us, and a son is given to us, and the government is upon his shoulder: and his name shall be called, Wonderful, Counsellor, God the Mighty, the Father of the world to come, the Prince of Peace."
Isaias (Isaiah) 9:6 ยท around 735 BC
Notice the two halves. A child is born: he is human, born like any baby. A son is given: he comes from somewhere else, given to us.
God the Mighty
Look at the names again. Wonderful. Counsellor. Prince of Peace. Those could describe a great king.
But "God the Mighty" can't. In Hebrew it's El Gibbor. And Isaiah uses the exact same title in the very next chapter, for the Lord himself:
"The remnant shall be converted, the remnant, I say, of Jacob, to the mighty God."
Isaias (Isaiah) 10:21
The child in chapter 9 carries the name of God in chapter 10. A baby, born to us, who is God.
On David's throne, for ever
"His empire shall be multiplied, and there shall be no end of peace: he shall sit upon the throne of David, and upon his kingdom... from henceforth and for ever."
Isaias (Isaiah) 9:7
Seven hundred years later, an angel told a young woman in Nazareth about her son:
"He shall be great, and shall be called the Son of the most High, and the Lord God shall give unto him the throne of David, his father: and he shall reign in the house of Jacob for ever, And of his kingdom there shall be no end."
Luke 1:32 to 33
Light in Galilee
Just before the child is announced, Isaiah says where the light would first be seen:
"...Galilee of the Gentiles... The people that walked in darkness, have seen a great light: to them that dwelt in the region of the shadow of death, light is risen."
Isaias (Isaiah) 9:1 to 2
Galilee, the region of Zabulon and Nephthali by the sea. It was despised, mixed with foreigners, the last place anyone expected anything from.
That's exactly where Jesus went to start preaching. He left Nazareth and lived in Capharnaum, by the Sea of Galilee, "in the borders of Zabulon and Nephthalim," and Matthew points straight back to Isaiah (Matthew 4:13 to 16).
Why this is a big deal
Isaiah didn't just predict a great king. He said a child would be born who would be called God, who would rule David's kingdom for ever, and whose light would dawn first in Galilee.
Seven centuries later, a child was born in David's line, began his work by the Sea of Galilee, and was worshipped as God. And his kingdom is still growing.