Exile is a punishment consisting of forced emigration from the victim's homeland, usually including the removal (or suspension) of citizenship - if any - and the forfeiture of fixed property (and sometimes moveable property as well). A exile's relatives may be permitted - or even forced - to accompany him, or they may be permitted - or obliged - to stay behind.
Exile may be de-facto (the offender is permitted to flee the jurisdiction in which he committed the offence) or official (whereby he is formally sentenced to exile) and may be for a limited period, for life or indefinite (the difference may be important if he dies and leaves heirs in exile). Exile may also be to a specific location (such as a penal colony1) or general (anywhere but "here").
If being made to go and live abroad doesn't sound like much of a punishment, consider that until very recently, citizenship was not treated as lightly as it is today, nor were people accustomed to leaving their native regions or being cut off from their kinship group. Exile was usually a way of forcing an opponent to live in poverty and ignomony as a second class citizen in a foreign land. It could also be very dangerous to the exile's home state if the wrong people were allowed to end up in the wrong places … such a rival heir to the throne at the court of a hostile foreign king.
Increasing international travel has made exile less popular as an offical punishment - and, indeed, many "receiving states" would object to having criminals dumped on them - but a great number of people still live in de-facto exile, whether in fear or persecution or prosecution.