What does Acts 13:24 mean?

To this point, Paul has been reminding a synagogue in Pisidian Antioch how God has saved the Jews throughout the history of Israel. He rescued them from slavery in Egypt, relented from judging their rebellion in the wilderness, and provided judges and kings to conquer their foreign enemies. Finally, God promised that a final Savior would come from the line of King David, a Savior that the famous John the Baptist announced was imminent (Acts 13:16–23).

Now, Paul must do the equivalent of turning a fully laden cargo ship. God chose the Jews as a people. He interacted with them as a nation. He promised them salvation as a group. John called the nation as a whole to repent. And God's promised Savior will sit on the throne of David forever. But not yet.

Jewish national leaders rejected their own Savior (Acts 13:27–29). So, despite Jesus' triumphal entry (Mark 11:1–10), He will not sit on David's throne yet. Paul will explain that God's Savior still offers salvation, but it is salvation from sins, not foreign oppression (Acts 13:38–39). And this salvation is offered freely to Gentiles as well as Jews. Paul would love it if the synagogue as a whole took John's offer to repent and Jesus' offer of salvation (Romans 9:3); sadly, they won't (Acts 13:44–52).

"Repentance" is from the Greek root word metanoia. It means to make a complete switch in paradigm, to admit you are wrong and Jesus is right. It is not a work, and it doesn't mean to ask for forgiveness. It is a change in understanding of the world, Jesus, and yourself, and a working desire to live according to God's commands. John's message of repentance was very popular among the people, but soundly rejected by the religious leaders in Jerusalem. They erroneously relied on their ethnic status as descendants of Abraham for their right standing with God (Luke 3:7–9). Paul will spend much of the rest of his life trying to explain that the children of God are not the descendants of Abraham but the followers of Jesus (Romans 11).