What does Luke 1:71 mean?

This is a citation of Psalm 106:10, which celebrated God's intervention for Israel at the Red Sea (Psalm 106:7–9; Exodus 14:28–30). The Exodus from Egypt was both a literal rescue from slavery and a powerful symbol of spiritual salvation (Galatians 4:3–5). That rescue proved God's promises to men like Abraham and Isaac were true (Exodus 6:8). Other guarantees came in the form of prophecies (Luke 1:70) about a Messiah (Isaiah 9:6–7) and a herald who would announce Messiah's ministry (Malachi 3:1; 4:6; Isaiah 40:3).

All these ideas are celebrated by Zechariah, a priest (Luke 1:5, 67). His wife has given birth (Luke 1:57) to the man later known as John the Baptist (Luke 1:13; 3:2–3). John's role will be to announce the Savior, Jesus Christ, whose impending birth was recently announced by an angel (Luke 1:31–33). Jesus' first coming to earth will establish a means for mankind to be saved from sin (John 3:16–17), while His second coming will establish an eternal end to all sin and evil (Revelation 19:11–15; 21:1–5).