Acts 25:20

And because I doubted of such manner of questions, I asked him whether he would go to Jerusalem, and there be judged of these matters.

Festus did not know how to handle the disputed questions of Jewish religion brought against Paul, and because of that uncertainty he asked Paul whether he was willing to go to Jerusalem and there be judged of those matters.
The accusations centered on questions of Jewish religion and on Jesus, whom Paul affirmed to be alive.
The proposal to move the trial to Jerusalem concealed a plot to kill Paul on the way.
Festus instead promised Paul a fair hearing at Caesarea, and God used that decision to preserve Paul's life.

These proceedings led to Paul's appeal to Caesar.
That appeal set in motion his eventual journey to Rome.
The delay before a suitable ship to Rome could be found gave Paul an opportunity to explain his faith to the leading men of Caesarea and to King Agrippa II.