Now the birth of Jesus the Messiah took place in this way. When his mother Mary had been engaged to Joseph, but before they lived together, she was found to be with child from the Holy Spirit.
The birth of Jesus of Nazareth to a virgin woman has been claimed by the Church from apostolic times, but it is today one of the most vexing claims about Christ that the Church grapples with.
I commend to your attention Tod Bolsinger's essay about the virgin birth. Among other things, Tod says that there was no expectation among first-century Jews that their Messiah would be born of a virgin. There is a passage in Isaiah in which the prophet is speaking to King Ahaz and tells the king,
Therefore the Lord himself will give you a sign. Look, the young woman is with child and shall bear a son, and shall name him Immanuel.
The King James and many later versions quote Isaiah, "... a virgin is with child," but this is a retrojection of Church tradition onto the Hebrew text. The Hebrew word used is alma, which simply means "young woman" with no indication of her marital status or sexual experience. Some scholars think Isaiah was referring to his own wife when he spoke to Ahaz, others that he was simply laying out a timetable for when Ahaz's troubles would be over. (Isaiah continued that by the time the child could eat solid food and choose between good and bad, Judah's foreign-policy problems would be gone.)
Since the Jews of Jesus day could certainly read Hebrew - it was taught in the synagogues, even though they mostly spoke Aramaic - they would not have ascribed virginity to the young woman of Isaiah's prophecy. In fact, the face reading of the passage is self-evidently against it! So Tod is right that no one of the time expected the Messiah to be born of a virgin. In fact, they didn't expect the Messiah to be born of the Holy Spirit, either. What they did expect was for the Messiah to be a powerful political ruler and military leader who would usher in an eschatological peaceable kingdom for the Jews.
However, Matthew quotes Isaiah thus:
"Look, the virgin shall conceive and bear a son, and they shall name him Emmanuel"
Matthew, of course, was written in Greek, and the word used for virgin is parthenos, which indeed means "virgin." The reason Matthew reads that way is that in 70 BC Jewish scholars in Alexandria translated the Jewish Scriptures into Greek. Their result is called the Septuagint, for "seventy," because the story is that 70 scholars worked nonstop for 70 days to make the translation. This translation is abbreviated LXX (Roman numerals for 70) and it was from the LXX that Matthew cited Isaiah. And the LXX uses the word parthenos in Isaiah where the Hebrew text uses alma.
There was no lack of myths or legends in the ancient world of miraculous conceptions and births. But there are profound differences between them and the story of the birth of Jesus. In most of the other stories, the encounter between the human parent and the god (or goddess) is presented graphically, even explicitly. What happens between the woman and the god is exactly what ordinarily happens between an ordinary husband and wife. But in Matthew’s story as well as Luke’s, God is not shown in the male role in conception. The Holy Spirit, the divine power and presence, works in Mary to conceive a child without a human father. There is no union between God and Mary, either in Matthew or in Luke. Jesus comes to exist as an unborn child simply because God wills it, not from anything God does to Mary. This distinction is perhaps a crucial one for understanding who Jesus was.
Let’s recall, for example, the story of the famous figure of Greek mythology, Achilles. Achilles was the son of a human father and a divine mother. Achilles’ portrayal in the Iliad shows that he was half human, half divine. He had much of the power and invulnerability of the gods, but the temper and tempestuousness of ordinary people. He led his men with godly courage, but carried out unforgivably harsh vengeance on the Trojan prince, Hector. Throughout the story, the tragedy of Achilles unfolded precisely because he was neither wholly god nor wholly human. He was half and half, and neither half was at peace with the other. His godly side strove for the higher virtues, but was dragged down by his humanity, and his divinity perverted his humanity. Thus, the story of the semi-divine, semi-human Achilles is one of tragedy.
Jesus is nowhere presented as a hybrid product of divinity and humanity. Jesus is not a half-and-half person. Jesus is affirmed as fully human and fully God, and his story ends not in tragedy at the cross but in victory at the empty tomb.
Tod observes that the virgin birth of Christ
... is God’s way of personally entering his creation. The Spiritus Creator that brought the universe into being, personally entered creation to bring restoration. God did not choose a human being, imbue that person with his Spirit and stick him on the cross (that view is called “adoptionism”). God himself did the job. God did not just send his Spirit, God himself saved us, was with us…
Mark D. Roberts has a thoroughly read-worthy series on whether the doctrine of Jesus's virgin birth is hype or history. Also, many people confuse the Catholic doctrine of the Immaculate Conception with the universal Christian doctrine of the birth of Jesus to the virgin Mary. But the are different ideas altogether.
The Immaculate Conception means that Mary, whose conception was brought about the normal way, was conceived without original sin or its stain - that’s what "immaculate" means: without stain. The essence of original sin consists in the deprivation of sanctifying grace, and its stain is a corrupt nature. Mary was preserved from these defects by God’s grace; from the first instant of her existence she was in the state of sanctifying grace and was free from the corrupt nature original sin brings.
However, this doctrine is exclusive to the Roman Catholic Church, having been promulgated only in 1854 by Pope Pius IX. Protestants have never worried about it.