Luke has a much different focus in his story of Jesus' birth. He begins with a feature common to his Gospel, alternating stories of men and women.
After explaining his serious historical inquiry, Luke begins with the story of an old priest whose wife could not have a child. We hear the OT stories of Abraham, Jacob and the parents of Samson in this account. It is a reminder that when God acts on behalf of His people it is wondrous and amazing. Zechariah, the priest, fails to trust the angel's message that he would have a child so he is struck mute. Is this Luke's way of illustrating that the voice of prophecy had been silenced in Israel for so many years? John the Baptist was considered the first real prophet since the close of the biblical canon by his contemporaries.
This is followed by Mary's visitation. She submits to God's plan. This is the first of many contrasts between John the Baptist and Jesus. Clearly Jesus is above John in Luke's narrative. Mary goes to visit her ancient, pregnant relative (Zechariah's wife Elizabeth). When she arrives, John the Baptist, still in his mother's womb, stirs. What follows is Mary's song. This is a central focus of the story. Herein lies the meaning of the event.
Mary glorifies God using words, phrases and images from numerous OT sources. In a sense the song of Mary is a composite of various other songs proclaiming God's saving activity. That is the key element of the faith journey. We cannot focus on ourselves, we must glorify God. Too often we wait for some amazing event to give us security and assurance. The pregnancies of these two women were not for private benefit. These boys will grow up to be The prophet and The Messiah. The pregnancies are for the nations! Mary sings that God will overturn the current world order. The mighty will be toppled. The poor and needy raised up. The political impact of the activity of God is earth changing. But God acts in love and justice, not petty political power plays. He raises up the lowly, but the goal is always to worship God alone and live a holy life. Reflecting on what is happening to her, Mary states what God is doing. He is bringing HIS kingdom. The pregnancy is but another step in that long process.