When a person is amoral, they couldn't care less if something is right or wrong. An amoral CEO fires employees so he can make more money, unconcerned about how losing their jobs might affect them.
The adjective amoral adds the prefix a-, "not," to moral, "concerned with the principles of right and wrong." Amoral people don't have a moral code — the morality or ethics of what they do doesn't matter to them, whether or not they're aware of the concept of right and wrong. Strictly speaking, you can even describe a newborn baby as amoral, since she doesn't yet have the experience to understand morality.