The Feast of the Annunciation, as the date of the Incarnation of Christ, was New Year’s Day in Christendom for hundreds of years, until the Gregorian Calendar moved it to January 1. The two New Year’s Days are referred to as Annunciation Style and Circumcision Style, for obvious reasons. I have long held that if you’re going to get circumcised, you might as well do it in style.
According to the Gospel of St. Luke (and you won’t catch me arguing with St. Luke), the angel Gabriel announced to the Virgin Mary (announce/annunciation, see how that works?) that she was to bear a son, reciting part of the ancient “Hail Mary” prayer, but leaving the rest for Mary’s cousin Elizabeth later in the chapter. “Blessed are you among women,” he said, which is an Aramaicky way of saying “You are the most blessed of women.” For this reason she is referred to as the Blessed Virgin Mary. Later when she meets with Elizabeth, she (Mary) prophesies that all generations will call her blessed. So if you call her blessed (and you should), you are fulfilling that prophecy—which certainly beats fulfilling some other prophecies I can think of.
After this odd greeting, Mary was puzzled. Gabriel, seeing her knitted brow, reassured her, saying, “Don’t freak out” (I’m paraphrasing), “God is pleased with you.” God is pleased with you. Stop and think about that. Go on to the next paragraph when you’re ready.
Gabriel however plowed right ahead with, “You’ll have a son, Jesus, he’ll be called the Son of the Highest and he’ll inherit the throne of David, and his kingdom will be everlasting.” Now watch what Mary says next. She doesn’t say, “What?! The son of the highest? The throne of David? Everlasting kingdom?” No, she says, “But I know not a man.” Now some people (I will not name any names) think she’s being naïve here, since just because she’s a virgin now needn’t mean she’ll be a virgin forever, and so on. The Church has taken her statement, however, to mean not just that she’s a virgin so far, but that she is committed to remaining so, and fully expects to do so. Gabriel is on the same page, and explains that she will conceive by the Holy Spirit, and thus her child will be called the Son of God. By way of example he holds up her cousin Elizabeth, who was barren into old age but now pregnant, as proof that God can do miracles. Our Lady’s response is, “I am God’s handmaiden. Let it be as you have said.” (One could be forgiven if one translated it, “Make it so.”)
And the rest is His story.
Why March 25? There was an ancient (and let’s face it kinda weird) tradition that great men died on the anniversary of their conception. Thus Our Lord’s conception was pegged to March 25 since that’s about when he died. (Why does Easter/Pascha slide and the Annunciation stand still, you ask? Don’t be pert or I’ll make you stay after and clean the delete keys.) Some church historians therefore think that Christmas was pegged on December 25 because that’s nine months after the Annunciation. Tell your obnoxious atheist friends to stick that in their Saturnalia/Sol Invictus argument.
At any rate, the day has been celebrated in the church since about the fifth century as the day of our Lord’s Incarnation. It is one of the Twelve Great Feasts in Orthodoxy, and a Solemnity in Catholicism. It’s thus Pretty Darned Important, no matter how you slice it.
Finally, those in the know would never forgive me if I didn’t mention that Tolkien re-wrote the Lord of the Rings in part so that the Fellowship leaves Rivendell on December 25, and the Ring is destroyed on March 25, wherefore Aragorn declares March 25 to be forever the beginning of the new year in Gondor.
 I finally get to use those two years of college Hebrew.