What does Acts 13:38 mean?

Paul and Barnabas are in a synagogue in Pisidian Antioch, near the center of modern-day Asia Minor. This is the fourth of five parts of Paul's address. The first was how God saved Israel in their past (Acts 13:16–25). The second was the story of Jesus' death and resurrection (Acts 13:27–31). The third was how Jesus' resurrection was promised in prophecy (Acts 13:32–37). Paul will end with a warning to accept Jesus or risk the punishment promised in prophecy (Acts 13:40–41).

In this fourth part, Paul faces his hardest task. To the Jews, "salvation" looks a lot like what Paul talked about earlier: rescue from slavery in Egypt, hardships in the wilderness, homelessness, and enemies (Acts 13:17–22). When God promised a Savior would come from David's line and John the Baptist declared that Savior was imminent (Acts 13:23–25), Jews naturally believed He would free them from Roman rule and bring the years of peace and prosperity the prophets promised. That didn't happen. The man who followed John died and, as far as the synagogue members know, that was the end of it.

Paul explains how Jesus of Nazareth is the Savior but He offers an even more complete type of salvation. Ultimate salvation from slavery, hardships, and enemies is still in their future. Now, Jesus offers salvation from sins. Paul has a hard time convincing his audience, but Jesus did, too. Early in Jesus' ministry, four men lowered their paralyzed friend through the roof while He was speaking. Jesus declared that the man's sins were forgiven. The scribes could not believe Jesus had the authority to forgive sins, so Jesus healed the paralyzed man, as well. Later, Jesus told His disciples how His death gave Him the right to forgive sins (Matthew 26:28); the resurrection acts as the accompanying miracle that proves His claims (Luke 24:45–47). Right before He ascended to Heaven, Jesus told the disciples to be His witness—to tell others about Him (Acts 1:8).

This is what Paul and Barnabas have come to do.