It is a medical condition and its proper name is anorexia nervosa.
People with anorexia nervosa avoid eating and lose a lot of weight. They often feel fat, even when they are very thin.
They may use other ways of staying thin, such as taking laxative tablets (which is dangerous and makes you go to the toilet more often) or by doing too much exercise.
They can become very weak, and without special help some people with anorexia can die.