Deportation means permanent exile from the United States. A person here illegally, or with a valid visa or green card, can be deported. If you have been deported, you cannot gain re-entry into the United States for at least five years. It is a felony if you re-enter before the end of the five years.
You can also be deported and permanently excluded from the United States if you have ever committed fraud or willfully misrepresented a material fact in order to obtain a visa
Aliens are deported, in most cases, for criminal activity. There are several categories of crimes that can result in deportation (or removal), in particular aggravated felonies, crimes involving moral turpitude (i.e. evil intent), drug crimes, and firearms crimes. Aliens can also be deported for domestic violence convictions.
INS judges do have some discretion in canceling removal. Cancellation most often occurs where the alien was a permanent resident for at least five years or has lived in the United States for seven continuous years after having been admitted under any status. However, if the alien has been convicted of an aggravated felony, deportation is a certainty. Someone facing deportation can also, in extreme cases, apply for asylum.
Keep in mind that having a close family relative who is a U.S. citizen (including a spouse or child) will not necessarily keep an alien from being deported, especially if the alien has been convicted of drug related or other very serious crimes.