Isaiah prophesied 700 years before the birth of Jesus.
However, he got a glimpse of the majestic birth even before it happened.
In Isaiah, chapters 7 through 9, Isaiah prophesies of the triumphant birth.
This sign from the heavens was enough to have people look forward to their future King, who would save them from their sins.
Isaiah 7:10-16 (KJV)
10 Moreover the Lord spake again unto Ahaz, saying,
11 Ask thee a sign of the Lord thy God; ask it either in the depth, or in the height above.
12 But Ahaz said, I will not ask, neither will I tempt the Lord.
13 And he said, Hear ye now, O house of David; Is it a small thing for you to weary men, but will ye weary my God also?
14 Therefore the Lord himself shall give you a sign; Behold, a virgin shall conceive, and bear a son, and shall call his name Immanuel.
15 Butter and honey shall he eat, that he may know to refuse the evil, and choose the good.
16 For before the child shall know to refuse the evil, and choose the good, the land that thou abhorrest shall be forsaken of both her kings.
What we learn: The Lord is God. A virgin shall bear forth a son. He is called Immanuel.
Isaiah 8:7-10 (KJV)
7 Now therefore, behold, the Lord bringeth up upon them the waters of the river, strong and many, even the king of Assyria, and all his glory: and he shall come up over all his channels, and go over all his banks:
8 And he shall pass through Judah; he shall overflow and go over, he shall reach even to the neck; and the stretching out of his wings shall fill the breadth of thy land, O Immanuel.
9 Associate yourselves, O ye people, and ye shall be broken in pieces; and give ear, all ye of far countries: gird yourselves, and ye shall be broken in pieces; gird yourselves, and ye shall be broken in pieces.
10 Take counsel together, and it shall come to nought; speak the word, and it shall not stand: for God is with us.
What we learn: The Lord is Immanuel. Immanuel means God is with us.
What both chapters mean: The Lord God shall be born of a virgin.
Isaiah 9:6-7 (KJV)
6 For unto us a child is born, unto us a son is given: and the government shall be upon his shoulder: and his name shall be called Wonderful, Counsellor, The mighty God, The everlasting Father, The Prince of Peace.
7 Of the increase of his government and peace there shall be no end, upon the throne of David, and upon his kingdom, to order it, and to establish it with judgment and with justice from henceforth even for ever. The zeal of the Lord of hosts will perform this.
What we learn: this baby is no ordinary man. The government is upon His shoulders. He is called Wonderful, Counselor, mighty God, everlasting Father, the Prince of Peace. His peace has no end. He is our judge and judges us with justice.
What the three chapters mean: The Lord God is coming as a baby boy. Immanuel is one of the names He shall be called. As we now know about His other names from Isaiah 9. From the beginning, this boy has been the Lord of the nations. While on earth or the heavens, He will continue to usher in peace to all nations. His wise counsel will continue to be heard in the ears of all those that seek Him. His judgment is not so far away and those that love Him, will have no fear.
Matthew 1:18-25 (KJV)
18 Now the birth of Jesus Christ was on this wise: When as his mother Mary was espoused to Joseph, before they came together, she was found with child of the Holy Ghost.
19 Then Joseph her husband, being a just man, and not willing to make her a public example, was minded to put her away privily.
20 But while he thought on these things, behold, the angel of the Lord appeared unto him in a dream, saying, Joseph, thou son of David, fear not to take unto thee Mary thy wife: for that which is conceived in her is of the Holy Ghost.
21 And she shall bring forth a son, and thou shalt call his name Jesus: for he shall save his people from their sins.
22 Now all this was done, that it might be fulfilled which was spoken of the Lord by the prophet, saying,
23 Behold, a virgin shall be with child, and shall bring forth a son, and they shall call his name Emmanuel, which being interpreted is, God with us.
24 Then Joseph being raised from sleep did as the angel of the Lord had bidden him, and took unto him his wife:
25 And knew her not till she had brought forth her firstborn son: and he called his name Jesus.
What we learn: The virgin Mary gave birth to a son by way of the Holy Ghost. Joseph called His name Jesus, as was directed by the Angel of the Lord. The prophesy of His name Emmanuel, was interpreted, God with us. For His people would proclaim that God was with them. As His believers do now.  Jesus, would then bear the sins of everyone, on the cross. He came into the world to save His people from their sins. Who are His people? Those that believe and follow Him.
What all the chapters mean: Matthew 1 is a fulfillment of the preceding chapters in Isaiah (7-9). The Lord God did come forth by way of a virgin birth. He saved His people from their sins. All those that believe in Jesus will be saved. They shall know His counsel and walk in His peace. The Lord God will judge the world but those that love Jesus will have no fear. For they shall be saved forever, with Him, in heaven.