It's an expression believed firstly used in theatre, typically said to actors or musicians before they go on stage, means "good luck"...come to common use in nowadays. Amongst all sorts of it's origins, one version says it might related to superstition. Back in those days, actors believed that there're bad goblins/spirits can hear their wishes, and then give the "bad luck"(the opposite of what you said) to whom you said "good luck" to. So people in theatre believed that to say "break a leg" will lead to "good luck" ... hope you have fun in learning ... :)

Off the top of my head: in the theatre it was considered bad luck to wish an actor "good luck" - so "break a leg" became the catchphrase instead.

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“Break a leg”当然不是指“断了一条腿”，某种程度而言，“break a leg”可被列为演艺圈、尤其是戏剧界的“行话”，朋友若要上台演出，你大可对他/她说：“Play well, Jack--break a leg!”（杰克，好运！祝你演出成功！） 　　究其渊源，这个颇为怪异的祝福语，有很多种说法。目前，较为大众接受的理论有两种。一种观点认为，“break a leg”源于莎士比亚时期的舞台传统。演出接受后，演员一般要到前台谢幕，如若表演出色，一般会赢得台下观众的“小费”。当然，接受了小费，演员是要弯腿行“屈膝礼”的。由此，“Break a leg”成了希望演员演出成功的形象说法。 　　还有一种观点带有浓厚的迷信色彩。传说人们非常相信精灵的存在，而这些精灵最喜欢制造争端。如果你许了个愿望，他们就会故意让相反的事情发生。于是人们要“祝愿某人好运”时，就会故意说“祝你跌断一条腿”，希望借此骗过那些精灵，让好运来临。

We say "break a leg" to someone who is about to give a performance. It's the same as saying "good luck!". We don't know exactly when or how this idiom started. One popular explanation is that it began in theatre. Many people who worked in theatres at that time were superstitious. They believed that it was UNLUCKY to say "good luck" to an actor who was about to go on stage. However, by saying "break a leg" to them, the opposite would happen and so they would have good luck. Hope this helped :)