There are no "buttons" for a judge to sentence a character to exile. It is a roleplay sentence. It means the other characters will probably persecute your character into compliance, such as with armies or court verdicts, which is allowed as long as the options of the verdict (prison, fine, death) comply with the Rules for the Administration of Justice (out of character limitations on sentences).
If you are sentenced to exile, it is likely that you have been very, very bad. Kind of mean. Or very stupid, but I won't judge. It could be for high treason, for example, because you're a captain of a duchy and you've provided the exact location and composition of the armies of that duchy to your buddies who are right on the border, ready to swoop in and plunder the territory. It's not right to do that. Not right at all. But since you have the right to do it and you have the right to be punished for doing it, I don't see the problem. It's up to you to take responsibility for your actions and accept the exile.
Have a good trip!!!