What does Luke 1:32 mean?

The angel Gabriel is explaining what will become of the Child born to Mary, a virgin (Isaiah 9:6–7) living in Nazareth (Luke 1:26–31). This miraculous conception will produce Jesus.

The title "Most High" is a reference to God. This is from the Greek hypistos, the same word Jewish translators would use when rendering the Hebrew term 'elyown. That is part of the Old Testament phrase 'El 'Elyon, literally meaning "God Most High" (Genesis 14:18–20). This phrase is an important part of Gabriel's message. Hebrew used the concept of a "son" to imply someone who had all the qualities of the father. Jesus, as the Son of the Most High God, will have all divine qualities (Hebrews 1:3). Both Jesus' friends (Matthew 16:16) and His enemies (Mark 5:7) will acknowledge this status. Jesus will claim it for Himself (Luke 22:70). All who properly understand Christ's divine nature will accept this, as well (John 1:49; 2 Corinthians 1:19).

God promised to send a Messiah through the line of king David (2 Samuel 7:12–16). This King from the future generations of David's family would provide ultimate, eternal victory for Israel (Isaiah 9:6–7). The last words of Gabriel's message reinforce this aspect of Jesus' role as Messiah (Luke 1:33; Psalm 45:6–7). Mary is of David's family line (Luke 3:23–38), as is the man to whom she is betrothed, Joseph (Matthew 1:1–17).

Mary likely understood both references and their implications. In a short pair of phrases, Gabriel is telling Mary she will give birth to God incarnate, the Savior promised by prophecy.