Exiling a noble is a power granted only to the ruler of a realm. It is generally considered a last resort. A way to try and deal with a noble who the judge can't, or won't, take care of on their own.
Exiling a noble essentially instructs the realm to not have any dealings with that noble. They will no longer be able to use the banks, recruiting centers, shops, or any other such realm infrastructure. Unlike banishment, however, they will not be removed from the realm. They will continue to be a noble of the realm until they choose to leave on their own. While they will continue to receive their taxes as normal, any bonds received will not be able to exchanged for gold.
Anyone can be exiled by the ruler, even those who cannot be banned. This includes Royals, other council members (include the judge), and nobles who are protected from banishment by their lords by good marks. This makes it a powerful tool for dealing with these otherwise untouchable nobles.
Exile is not, however, without its own cost. It is a test of wills between the ruler and the exiled noble. For so long as the exiled noble remains within the realm, the ruler will slowly lose both honor, and even prestige. This gradual loss will only end when either the exiled noble leaves the realm, or the ruler steps down from the throne.
Once exiled, a noble can no longer be banned. The contest between the ruler and the exiled noble can only end when one of them admits defeat.