The word "bust" has several meanings depending on the context in which it is used. Generally, it refers to the upper part of a person's torso, particularly the area around the chest and breasts. In another context, "bust" can mean to break or smash something. Additionally, "bust" can denote a situation where someone is caught in an illegal act or a failure of a plan.
The word "bust" comes from Middle French "buste," which means "a statue of a person’s head, shoulders, and upper chest." This in turn comes from Italian "busto," which translates similarly. The usage of "bust" to mean to break something has origins in the colloquial use that developed later in English.