It is tempting to highlight the lowliness of Jesus when reading the infancy stories of Luke. However, Luke stresses his greatness rather than his commonness.
When Gabriel appears to Mary, he gives these details concerning her son.
1) His name will be Jesus. In Hebrew it is either Yeshua, or Yhoshua (Joshua), a very common name. But the context shows that the significance of the name is not that it was a common one, but in its meaning which is "deliverer."
2) He will be great. Even though he had a common name, he would not be a common person. But his greatness would demonstrate itself in a way many would not expect.
3) He will be Son of the Most High. "Most High" was one of the designations for Yahweh in the Old Testament. In Hebrew, "ben-" (son of) sometimes designated a category. In other words, if you were "Ben-Adam" you would be "Son of Man," which simply means human. If you were "Ben-Elohim" you would be "Son of God" which means you were divine. Even though Jesus was going to be born of a woman, he would also be divine.
4) He would have the throne of his ancestor, David. This is an allusion to 2 Sam 7:12-13 where God promised to set David's descendant on the throne and he would establish the throne of his kingdom forever. So, Mary's son would be a king.
The Bible is no stranger to unusual births. For example, there was Samuel, Samson, Isaiah's son, and John the Baptist.. Then of course, there is the famous unusual birth of Isaac. In response to Abraham's and Rebekah's difficulty believing a couple their age could have children, God asked a rhetorical question.
"Is anything too difficult for the Lord?...(Gen 18:14)"
Nothing is impossible with God. God proves this by doing something totally unlike anything he has done before. When Gabriel tells Mary she will have a child, she is puzzled, wondering how this will happens since she had never been with a man. With that, Gabriel says,
"The Holy Spirit will come upon you, and the power of the Most High will overshadow you; and for that reason the holy Child shall be called the Son of God. ... For nothing will be impossible with God (Luke 1:35-37)."
Nothing is impossible with God. There is no question that this child is from God. Elizabeth having a child in her old age is amazing enough, but an unmarried virgin with a child is unheard of! God is all-powerful and concerned about us! Therefore, all things are possible with God.
In this story, we see the common intersect with the holy, the powerless with the omnipotent, greatness with the humble. He doesn't go to an aristocratic family in Jerusalem. The Lord of creation comes to an obscure village like Nazareth to a young teenage girl.
Luke doesn't stress his lowliness, but his greatness. Jesus comes to the humblest place in the land and he lifts up the humble. No matter how insignificant we are, we are not insignificant to him. Our Lord modeled humility in a unique way. We should follow his example of humility and reach out and lift others up as well (Phil 1:1-7).