What does Acts 13:12 mean?

Paul has freed the proconsul of the island of Cyprus, Sergius Paulus, from the lies of his fraudulent spiritual advisor Bar-Jesus (Acts 13:6–11). Bar-Jesus is a Jewish false prophet who cheated Sergius Paulus instead of leading him to the local synagogue to learn about God. Paul and Barnabas met Bar-Jesus first; it's not explicitly clear how the proconsul heard about them or why he invited them to speak. He may have heard that they were introducing a new Jewish sect to his people and wanted to know if they were a threat. But when faced with the truth about Jesus and the power of the Holy Spirit he quickly rejected his corrupt spiritual advisor and accepted the spiritual truth Paul offered.

There is an inscription mentioning Lucius Sergius Paulus in Antioch in Pisidia, near the center of Asia Minor. This Antioch is Paul and Barnabas' next major stop. It's possible the proconsul asked they go to Antioch to spread the gospel to his family, and also possible he gave them letters of introduction. If he did, they weren't sufficient (Acts 13:50).

Caesar Augustus portioned off the Roman Empire into provinces that were senatorial or imperial. Senatorial provinces were ruled by a proconsul instead of a king and did not quarter legions for defense. Sergius Paulus had to be intelligent to rule peacefully without an army to back him up (Acts 13:7). The fact that he seemingly fell for Bar-Jesus' lies shows how desperate he was for God.