What does Acts 13:17 mean?

This is the only one of Paul's many synagogue sermons directly recorded in Scripture. This first of five sections recalls God's saving work in the history of Israel. Here, Paul recounts the popular story of how God saved the Israelites from slavery by leading them out of Egypt. The middle of the section will show how God acted to establish the nation and save the national identity. Finally, Paul reminds his audience of how God promised to send a Savior to sit on David's throne forever (Acts 13:16–25).

The "fathers" God chose were Abraham, Isaac, Jacob, and Jacob's sons. Despite the brutal conditions in Egypt, the people became "great"; when they left, they had about 600,000 men and additional women and children (Exodus 12:37). The "uplifted arm" may mean God's power, but may also refer to Moses' arm which held his staff aloft to herald God's action of parting the Red Sea to allow the Israelites to cross and held it again as God allowed the waters to drown Pharaoh's army (Exodus 14:16, 21, 26–27).

Paul will go on to explain how the Jewish leadership rejected God's Savior, how God saved His Savior from the grave, and the spiritual nature of salvation, as well as warn the Jews and devout Gentiles to accept God's Savior (Acts 13:26–41). Some of the Jews and many of the Gentiles will accept the Jewish Savior, but the Jewish establishment as an organization will not (Acts 13:42–52).