What does Acts 25:3 mean?
The Sanhedrin has been waiting for two years to get their hands on Paul. Their moment came, but in a disastrous meeting during which Paul insulted the high priest—possibly by accident—and manipulated the council factions into fighting against each other. Next, they tried an assassination attempt, but were foiled by Paul's nephew who overheard the plot (Acts 23:1–15). Then they presented evidence of Paul's crimes before Governor Felix, but Felix refused to convict Paul. His reasons were glaringly obvious: the Sanhedrin had neither evidence nor witnesses (Acts 24:1–9).Instead of handing Paul over to the Sanhedrin, Felix kept him under house arrest in Caesarea Maritima. That kept Paul out of the way, but it also kept him out of the Sanhedrin's clutches (Acts 24:22–27).
Now there's a new governor in town: Festus. He doesn't seem aware of the failed assassination attempt or the botched trial, but he's eager to please. The council members see their chance. They officially request a favor: that Festus hold a new trial in Jerusalem. Festus counters with a preliminary hearing in Caesarea. He invites representatives to come and present their evidence. If he finds they have a case, he'll see about getting Paul to Jerusalem (Acts 25:4–5).
The Sanhedrin doesn't care about the court case. They care about one thing: if Festus agrees to a trial in Jerusalem, he will have to transport Paul the long distance from Caesarea. The assassins will finally have another chance to take Paul out.