What does Acts 25:15 mean?

Governor Festus is explaining Paul's case to Agrippa II in hopes the king can help.

A few weeks before, three days after Festus arrived at his new assignment, he traveled to Jerusalem to meet the Sanhedrin—the ruling Jewish council. They asked him to send Paul to Jerusalem so they could try him for crimes against the Mosaic law. Festus reversed the invitation, telling them to send representatives to Caesarea Maritima to present their evidence. They did so (Acts 25:1–5).

They claimed Paul had started riots all over the Roman Empire, that he desecrated a religious structure, and that he leads an illegal cult (Acts 24:5–6). All of these were crimes against the Roman law and could be capital offenses. Paul countered by simply saying no, he didn't do any of that. Since the Sanhedrin provided no witness or evidence, Festus knew Paul was innocent, but he wanted to please the Sanhedrin, so he asked Paul if he wouldn't mind going to Jerusalem for trial. Since Paul was a Roman citizen, he had the right to choose whether to have the trial in the city where the crimes allegedly took place—Jerusalem, the city where the judge resides—Caesarea, or his home city—Tarsus. Festus happens to have jurisdiction in all three places and Paul had no desire to move and be the target of another assassination attempt (Acts 23:12–15; 25:3). He chastised Festus for not taking responsibility for his office and appealed his case to Caesar (Acts 25:6–12).

Now, Festus must send Paul to Caesar in Rome as a prisoner prepared for trial, but Paul has committed no crime. Festus asks Agrippa for help: what should he say Paul has done?

The Sanhedrin is the group of priests, scribes, and elders who regulate and judge the application of the Mosaic law. The council is often identified as "the Jews" or "the chief priests and elders."

"Chief priest" is not a God-ordained designation. God established the priests as the qualified descendants of Aaron and the high priest as the single man in authority. During the time between the Old and New Testaments, the office of priest became politicized and "chief priest" became a title of a priest who had significant authority, often because of family ties.

An "elder" was often a prominent businessman from around Jerusalem. Moses used a version of this office on the advice of his father-in-law to see to minor interpersonal issues that needed to be judged but didn't require Moses' direct intervention (Exodus 18). Elders of cities and villages typically made themselves available at city gates for the people to seek their advice or supervise legal transactions (Ruth 4:1–2).