What does Acts 16:31 mean?

The previous day, the city magistrates in Philippi beat and imprisoned Paul and Silas for sharing Jesus' story. That night, an earthquake freed them and the other prisoners from their cells. They all stayed, saving the jailer from execution. Now, the two explain how Jesus offers forgiveness of sins, saving the jailer and his family from eternity in hell (Acts 16:20–30).

In the Roman Empire, people typically prayed and offered grain to household idols for the good of the family. Each city had specific gods the people were expected to worship so the region would be blessed (Acts 19:28). The Empire had dozens of gods, including the emperor, all of whom needed to be placated. Beliefs on the resurrection of the dead depended on one's philosophical school. Only the Jews were authorized to worship an invisible God, and they were called "atheists" for doing so. But some philosophers were functional atheists, denying the existence of the supernatural but only in secret for fear of persecution.

With all these different worldviews, it's understandable the jailer would ask Paul and Silas how to be saved. They introduce him to the invisible Jewish God and the visible Jesus of Nazareth, Son of God, who died for the sins of the world, was resurrected, and now offers forgiveness to all who have faith to accept it. They explain how His offer is not because anyone deserves it—no one does—but because God has grace to save (Ephesians 2:8–9).

Paul will later describe how he takes pride in his ability to adapt to any situation: whatever is needed to share Jesus' offer of salvation (1 Corinthians 9:19–23; Philippians 4:11–13). As he says in 1 Corinthians 9:23, "I do it all for the sake of the gospel, that I may share with them in its blessings." Sitting in the home of his jailer, blood drying on his skin, knowing he will have to leave the city in the morning, Paul shows no condemnation. If given half the chance, nothing will keep him from sharing Jesus' love.