A fire-eater is a person in a show — circus, street, night market — who puts a burning stick or torch into their mouth and seems to swallow the flame. They do not eat fire in the ordinary sense. They train so the flame goes out in a wet mouth without burning them; it is a skill, and it is still dangerous. The word is informal in the sense that you meet it around entertainment, not in science class. Older writing sometimes stretches it to mean a fierce, angry speaker, but students will almost always meet the circus meaning first.