Jesus
Why does the virgin birth matter?
Beyond fulfilling Isaiah's prophecy as Matthew presents it, the virgin birth is theologically significant mainly because of what it says about who Jesus is: it marks the incarnation as a genuinely unique event, God the Son entering human life from its very beginning, fully human and fully divine from conception, not becoming divine at some later point.
Christians have also connected it to Jesus' sinlessness, though traditions differ on the exact mechanism—some see the virgin birth itself as the means by which Jesus avoided inheriting a sinful nature, while others locate that more in the direct involvement of the Holy Spirit than in the biological absence of a human father specifically.
It's worth distinguishing this from the Catholic doctrine of Mary's Immaculate Conception, which is a separate, distinctly Catholic teaching about Mary's own conception being kept free from sin—not shared by Protestant or Orthodox Christians, who affirm the virgin birth without holding that additional doctrine.
Bible quotations in these answers are generally taken from the Christian Standard Bible®, Copyright © 2017 by Holman Bible Publishers. Used by permission. Christian Standard Bible® and CSB® are federally registered trademarks of Holman Bible Publishers. Some biblical wording may be paraphrased or follow other translations.