"After spending eight or ten days with them, he went down to Caesarea, and the next day he convened the court and ordered that Paul be brought before him." NIV translation
In chapter 9, we saw God tell Ananias that Saul (Paul) would "carry my name before the Gentiles and their kings". This is coming to pass as Festus opens the trial in Caesarea. God has also decreed things about each and every one of us (see Ephesians 2:10) and, just as God called Paul to appear before kings, He has things for you and I to do as well.
"When Paul appeared, the Jews who had come down from Jerusalem stood around him, bringing many serious charges against him, which they could not prove." NIV translation
For the third time, the Jews made charges against Paul without any proof that he did anything wrong. It seems that some people do not let the facts get in the way of their opinion. Jesus and Paul were both persecuted and we can look forward to that as we serve the Lord. In order to face these struggles, we should prepare as Paul taught in Ephesians 6.
"Then Paul made his defense: 'I have done nothing wrong against the law of the Jews or against the temple or against Caesar.'" NIV translation
Paul's answer to the charges was a simple statement of the fact that he had done nothing wrong. He did not argue with them as most of us would probably do. If your heart is clean, then you do not have to argue with those that oppose you.
"Festus, wishing to do the Jews a favor, said to Paul, 'Are you willing to go up to Jerusalem and stand trial before me there on these charges?'" NIV translation
Festus was a politician and so wanted to make the Jews happy by giving them what they wanted which was a chance to ambush and kill Paul. We do not know if Festus knew about their plan but he probably did not care. He had all of the interested people assembled and could have simply had the trial then and there.