What does Luke 1:51 mean?

Mary is praising God for His gift of the Messiah, Jesus Christ, and her privilege of being His earthly mother (Luke 1:31–33). She has honored the Lord for His role as her Savior (Luke 1:46–47), His favor in entrusting her with this role (Luke 1:48), His holiness and power (Luke 1:49), and His promise to show mercy to those who love Him (Luke 1:50). These statements are drawn from various places in the Old Testament, either as quotations (Psalm 103:17) or direct references (1 Samuel 1:11; 2:1; Psalm 50:1; 99:5).

In this verse, she continues to proclaim God's attributes. References to the "arm" were commonly used as a metaphor for strength, especially in battle. God has already proven His power over earthly enemies (Psalm 89:13; 98:1). With the coming of the Messiah, He will begin to complete that victory (Isaiah 9:6–7).

Likewise, Mary had already seen evidence that God could bring arrogant people to humiliation (Daniel 4:37; Isaiah 2:17; Proverbs 21:4). New Testament writers would later note that the ministry of Christ overturned the world's conceited view of its own knowledge (1 Corinthians 1:20, 27–31).