Felix holds a hearing of both sides. The Jews accuse Paul of instigating unrest, the one thing Rome can't stand. Paul defends himself ably: he's done no such thing, but believes the Law and Prophets as every good Jew does. Felix stalls, hears Paul more often, is convicted by him, but leaves him in jail as a favor to the Jews.
Festus also wants to do the Jews a favor by handing Paul over to him. Paul argues correctly, and well, that Festus has no right to do that as he appeals to Caesar. Herod Agrippa arrives and Festus talks shop with him, about Paul's case, wondering what to tell Caesar about Paul. So Agrippa hears Paul, too. (Perhaps a sly move on Festus' part: pretending to seek Agrippa's wisdom, while sloughing off responsibility for what to tell Caesar to Agrippa.)
Paul again grounds his defense in the orthodox Jewish Pharisee's resurrection hope, fulfilled in Christ. He also describes his mission to the Gentiles, preaching forgiveness of sins in Jesus. Agrippa and Festus are both somewhat convicted. Agrippa's words are a rebuke to Festus for making Paul appeal to Caesar when Festus offered (threatened) to hand Paul over to the Jews.