There are a lot of possibilities as to the origin of this phrase. One possibility goes back to ancient Greece. Greek citizens used to stomp their feet when they enjoyed a play instead of clapping their hands. If the audience members stomped their feet hard enough, it was believed that someone would eventually break a leg. So when an actor says “break a leg” to another actor, they are hoping that the actor’s performance garners overwhelming appreciation from the audience. Another possible origin of this phrase comes from the days of vaudeville. In vaudeville, when an actor gets to appear onstage, it’s called breaking the leg of the curtain. An actor who breaks the leg of the curtain has the good fortune of getting paid for that night’s performance. This phrase is still widely used in the performing community today.

Source: Theater Seat Store