About two decades before the birth of Christ, Rome passed a law, the lex de ui publica, which forbade any magistrate to kill, scourge, chain, torture, or even sentence a Roman citizen who had announced his intention to appeal, or prevent him from going to Rome to lodge his appeal there within a ﬁxed time.
Acts 25:11 If, however, I am guilty of doing anything deserving death, I do not refuse to die. But if the charges brought against me by these Jews are not true, no one has the right to hand me over to them. I appeal to Caesar!"
Did it mean that Paul would actually see the Emperor in person?
Assuming (for a moment) that Paul’s case did come to trial, it is very unlikely that the case was heard by Caesar Nero. The Emperor, according to Tacitus, had been quite ﬁrm in the matter of rendering judgments: “‘He would not’ [Nero] said, ‘be judge in all cases…’.”54 Up until a.d. 62 or 63 he made no exceptions, and only a few after that time, up until the burning of Rome. Appeals cases were apparently assigned to various ofﬁcials.
Could Paul withdraw it after saying it?
Acts 26:32 Agrippa said to Festus, "This man could have been set free if he had not appealed to Caesar."