What does Acts 18:13 mean?

At least since the time of Jeroboam, rulers have known that if you can control what gods people worship, you can keep the people united (1 Kings 12:26–29). The Romans knew this, too. About a hundred years before Paul ministered in Corinth, Cicero wrote a fictional dialogue about natural law and the religious law of Rome. In De Legibus ii.8, he writes, "…let no one have private gods—neither new gods nor strange gods, unless publicly acknowledged, are to be worshipped privately…" By this, he means it should be against the law to worship gods not endorsed by the Roman government.

So, when the Jews of the synagogue in Corinth can't get Paul to stop teaching that Jesus is the Son of God, the Messiah who offers reconciliation with God, they bring him before Gallio, the proconsul. There, they accuse him of breaking the Roman law that forbids the teaching or worshiping of a god Rome has not authorized. If they succeed, they will have won a great victory; a proconsul, under the authority of the Roman Senate, has the power to control where Paul can go throughout the Empire.

Unfortunately for the Jews, Gallio doesn't care. He doesn't see the difference between the God Paul preaches and the God the Jews worship. Or, at least, he does not see that the differences are meaningful with respect to Roman law. The Roman government already authorized the Jews to worship their God, so Gallio tells them, "since it is a matter of questions about words and names and your own law, see to it yourselves. I refuse to be a judge of these things" (Acts 18:15).

Gallio not only refuses to charge Paul, he does nothing when a crowd grabs the leader of the synagogue and beats him in the middle of the court. Paul stays in Corinth for eighteen months, building up the church he has planted, knowing that when God makes a decision (Acts 18:9–10) He can use whatever means He wishes to fulfill it.