The Bible clearly teaches us that Jesus Christ, the Son of God, was born to Mary who was a virgin. Why is this important?
It is important for many reasons. First, the Bible is God's inspired Word. So if something is clearly stated, especially repeatedly, in the Bible, God has a reason for communicating this, and we should believe it!
Another reason it is so important is that Jesus Christ was both the Son of God and the Son of Man. Jesus was divine -- He was God in the flesh. He was also human -- He was born to a human mother. So He is the Son of God and the Son of Man. Our human minds cannot truly comprehend this, but this is important for us to know.
Jesus was born without sin. Ever since Adam and Eve, we have all sinned; we both choose to sin, and in some ways, we inherit a sinful nature from our first father, Adam. The fact that Jesus' Father was God meant that He did not inherit the sinful nature from Adam.
Another reason it is important is that Jesus' birth was a true miracle. The angel spoke to Mary that she would have a son without having relations with a man, and with man, it is impossible, but with God all things are possible.