So has the Lord done for me at a time when he has seen fit to take away my disgrace before others. The conception and birth of John the Baptist is, in some respects, similar to that of his cousin Jesus which it serves to introduce (the birth of John the Baptist pre-figures that of Jesus Christ). It was not a random choice that God chose Zechariah and Elizabeth to be the parents of Jesus’ forerunner. God was making a statement. It was a statement that made clear what the mission of Jesus Christ was going to be, something that Elizabeth sums up in her words quoted above.
Up until the conception of John the Baptist, Elizabeth was childless. Because of her age, she was considered barren since any hope of her ever conceiving and giving birth had dried up when she crossed that threshold. In the eyes of other women and the community at large, she was a cursed woman. She (or her family) must have done something which had ‘forced’ God to mete out such a harsh punishment upon her and her husband. Upon their deaths, Elizabeth and her husband Zechariah would have had no one to ‘carry their names’ through subsequent generations. Their names would have followed them to their graves where they would be buried and forgotten. Theirs would have been real ‘deaths,’ for they would have left behind no one to remember them. It was a misfortune about which childless women would have been reminded on a daily basis even as some would use their condition to shame and torment them (cf. 1 Samuel 1:6-7). One can thus understand the joy with which Elizabeth greeted her coming to knowledge of the good news that she was expecting a child (no wonder she went into exclusion for five months!)
Elizabeth’s joy prefigured the joy which would soon surround and accompany the birth of the Lord and Savior of the universe, Jesus Christ. To borrow the words of Zechariah, the birth of Jesus Christ was going to mark a new dawn for countless men and women (cf. Luke 1:78). There were many men and women who, just like Elizabeth, were reminded on a daily basis of their misery and misfortunes. These men and women were not only looked down upon by the society but were also considered as unworthy of God. Like a childless woman, these little ones would be shamed and tormented on a daily basis for something that was not their own doing. But just like in Elizabeth’s case, their fortunes were soon going to be reversed. In Jesus Christ, these sons and daughters of God were going to find a friend and someone who would care about their wellbeing. In Jesus Christ, the Lord was going to visit them. It was on behalf of them that Elizabeth spoke those words of praise and thanksgiving since in Jesus Christ, God was going to take away their shame and disgrace. 
May the celebration of the birth of Jesus Christ be a joyful occasion for us who are eagerly awaiting it. May the celebration remind us that God has found us worthy to host him. No longer should we feel ashamed of ourselves or of what is going on in our lives. Jesus Christ, our saving Lord, has come to take away our disgrace.