What does Acts 18:14 mean?

The Jews of Corinth are using an old but effective method to shut down the worship of Jesus: Roman law. Years before, the Sanhedrin accused Jesus of placing Himself as king above Caesar. Pilate didn't believe them, but he feared their ability to disrupt Jerusalem and make him look ineffective, so he bowed to their wishes and had Jesus crucified (Luke 23:1–25; John 19:12–19). Now, Paul stands accused of preaching and worshiping a deity—Jesus—not pre-authorized by the Roman government. One hundred years before this trial, Cicero wrote, "…let no one have private gods—neither new gods nor strange gods, unless publicly acknowledged, are to be worshipped privately…" in De Legibus, his discussion about the Roman law. If the Jews can convince Gallio, the proconsul of Achaia, that Paul is an enemy of the state, he could restrict Paul's movements in the Roman Empire, or at least expel him from Corinth.

Unfortunately for the Jews, Gallio doesn't care. As far as he's concerned, Christianity is a Jewish sect. It's a religious matter, not a civil issue. He tells them to handle it themselves. When Paul went to the synagogue first and convinced several Jews—including the ruler of the synagogue—Christianity effectively became a civilly-protected religion (Acts 18:4, 8).