What does Acts 25:12 mean?
Everyone wants something different. Porcius Festus, the new governor, wants a good relationship with the Jewish leaders. The previous governor had been cruel and violent. Festus would rather keep the peace by working together. He's inclined to give the Sanhedrin what they want if he can.The Sanhedrin wants Paul dead. They failed two years ago (Acts 23:12–15), and they want another shot. If they can convince the new governor to send Paul to Jerusalem for trial, Paul can come to an untimely end along the way (Acts 25:3). Festus is only useful to them so far as he gives them what they want.
Paul wants to get out of Caesarea Maritima where he's been in custody for the last two years. Preferably, he'd like to be freed, but if that isn't going to happen, he can at least escape the Sanhedrin. When he realizes he can't trust Festus to do the right thing and clear the Sanhedrin's baseless charges, he appeals his case to Caesar (Acts 25:11).
This is almost as good for Festus as it is for Paul. Paul's fate is out of his hands—the Sanhedrin can't fault him for following Roman law. But now he has a new problem: what is he going to tell Caesar? Paul didn't do anything except argue about religion (Acts 25:19). He shouldn't have been kept for two years. Festus can't send Paul to Nero without a reason (Acts 25:26–27).
Luckily, Festus finds an ally. After a few days, King Agrippa II and his sister Bernice arrive, and they agree to listen to Paul and help determine his crime. Festus includes all the noblemen of Caesarea (Acts 25:23). Paul is not only allowed to give his testimony to Agrippa and the leaders of the district, but he nearly converts Agrippa. Agrippa agrees that Paul has done nothing, but they must honor Paul's request and send him to Rome (Acts 26).