Exile or banishment was a type of action or punishment in which a person must leave their home and was forbidden to return. Exile might also be self-imposed.
Following Harry Mudd's capture following the events that occurred on Rigel VII in 2266, Mudd requested that perhaps, "by accident", James T. Kirk could "arrange to leave me behind" on the planet, stating that "On this planet that would be punishment enough." (TOS: "Mudd's Women")
Exile was a popular method of punishment used by the Cardassians. Famous people to be exiled from Cardassia include Iloja of Prim and Tavor Kell. Iloja settled on Vulcan where Tobin Dax met him. (DS9: "Destiny", "The Muse")
Major Kira Nerys hoped that Tekeny Ghemor would set up a Cardassian government-in-exile on Deep Space 9 to oppose the newly Dominion-controlled Cardassian Union. The plan was abandoned, as Ghemor was terminally ill with Yarim Fel Syndrome. (DS9: "Ties of Blood and Water")
Elim Garak was exiled as well, although the reasons are unknown. Several reasons he told for his exile included destroying a Cardassian shuttle, that he had showed mercy and let several Bajoran children escape interrogation, that he had been betrayed by "Elim" and that he had not paid his taxes. (DS9: "The Wire", "Improbable Cause") The reasons for Garak's exile may be unknown, but Enabran Tain was involved. (DS9: "In Purgatory's Shadow")
Garak had a chance to end his exile in 2370, by apprehending Natima Lang, Hogue and Rekelen on Deep Space 9, but chose not to, after finding out that Gul Toran had tricked him. (DS9: "Profit and Loss") Garak's exile finally ended in 2375. (DS9: "What You Leave Behind")
The Doctor commented that the great defender Torelius would go into voluntary exile if he were alive to see his sports team, Mountain, performing so poorly in the current season. (VOY: "Blink of an Eye")