“…for He who is mighty has done great things for me, and holy is His name” (Luke 1:49).
What are those great things the Lord has done for the Blessed Virgin Mary? Luther explains well:
The “great things” are nothing less than that she became the Mother of God, in which work so many and such great good things are bestowed on her as pass man’s understanding. For on this there follows all honor, all blessedness, and her unique place in the whole of mankind, among which she has no equal, namely, that she had a child by the Father in heaven, and such a Child. She herself is unable to find a name for this work, it is too exceedingly great; all she can do is break out in the fervent cry: “They are great things,” impossible to describe or define. Hence men have crowded all her glory into a single word, calling her the Mother of God. No one can say anything greater of her or to her, though he had as many tongues as there are leaves on the trees, or grass in the fields, or stars in the sky, or sand by the sea. It needs to be pondered in the heart what it means to be the Mother of God.
LW 21:326

That being the Mother of God is the great thing God has done for her is strengthened by Elisabeth’s own confession, for Elisabeth is the first human being to call Jesus “Lord,” that is, to identify Him as the Lord Yahweh. John the Baptiser was conceived first. After she had conceived John, Elisabeth said, “Thus, the Lord has done for me in the days when He looked on me, to take away my reproach from among people” (1:25). The Jews always and only referred to Yahweh as Adonai (Lord). Then, in the sixth month of Elisabeth’s pregnancy (vv. 26, 36), Mary is told she will conceive the Saviour and she visits her relative, Elisabeth. During this visit, Elisabeth’s baby leaps in her womb at the mere sound of Mary’s voice, she is filled with the Holy Spirit, and she proclaims the Hail Mary, “Blessed are you among women, and blessed is the fruit of your womb! And why is this granted to me that the mother of my Lord should come to me? (vv. 42-43). She identifies the baby in Mary’s womb as her Lord, Yahweh.
The Trinitarian implications are strong here. Jesus is not the Father or the Holy Spirit, but the Son. Yet like the Father and the Holy Spirit, He is co-equally God. (This mystery is unfathomable.) Therefore, Mary gave birth to God, that is, God the Son—Yahweh the Son. (This is also a mystery.) Of all mothers to have ever lived, the fruit of her womb is the most blessed, indeed, the most holy. Having given birth to our Lord and Saviour, she is to be venerated and honoured above all mothers. It could perhaps be argued that she is our Mother if we are indeed brothers of Christ (Romans 8:29; Hebrews 2:11-12), just as the Church is our Mother.
Yet our honouring her ends with the veneration; we do not pray to her or ask her to pray for us since “there is one God, and there is one mediator between God and men, the man Christ Jesus” (1 Timothy 2:5). She is worthy of our honour because of the honour God bestowed upon her as the theotokos (Mother of God), but not of our praise in prayer since that belongs solely to our one God, Jesus Christ.