Other forms: broke a leg; breaking a leg; breaks a leg
It may sound nice to wish an actor good luck on their stage debut, but it might actually be kinder to tell them to break a leg.
The most likely theory for this mysterious phrase's origin comes from the idea that certain things are unlucky to say or do in a theater. In a theater, wishing someone good luck might jinx them instead. To reverse this, you could wish something bad to happen to a person, which might bring them good things instead. This inversion isn't limited to English: in German, you can say Hals- und Beinbruch, meaning "break your head and legs," to wish a person good luck.