Someone who is amoral is one that does not know the difference between that which is right and that which is wrong. More and more western society is becoming amoral, as morality is taught as something that is relative to the situation.
Legally, Amorality is reffered to as "insanity" when the person is incapapable of knowing right and wrong.
Amorality is not to be confused with immorality, in which the individual does have a sincerely held moral code, but that moral code is actually immoral in itself. For instance, Al-Qaeda is immoral, not amoral, because they morally believe that since America is evil, they are religiously required to annhilate it. Although this is immoral, Al-Qaeda sincerely believes it is moral, and thus has a sense (albeit a deformed one) of morality. Amoral individuals, on the other hand, have no moral code whatsoever.
In other cases, a person that is immoral chooses to do that which is wrong, knowing full well that it is wrong. For instance, a poor person might rob someone else, knowing it is wrong, but needing the money.
In many ways amorality is more dangerous than this type of immorality. A person who knows they are lost can turn to what is right, such as the poor robber finding a job so he can afford to buy food with his own money. Additionally, someone with a deformed, but sincerely held, moral code could see the err of his ways and change. However, a person who has lost their compass entirely will have a hard time finding their way at all.