Why is it significant that Christ was conceived by a virgin?

The prophecy in Isaiah 7:14 points to the virgin birth as a miraculous sign indicating that the Messiah would be born without sin. This is significant because Christ, being conceived of the Holy Spirit and born of a virgin, did not inherit the sinful nature that all other infallible humans carry. This allowed Him to fulfill the law perfectly, as He was God incarnate, thus bridging the gap between divine righteousness and human sinfulness. By being born sinless, He could serve as the perfect sacrifice and redeemer for His people.