Breaking joints basically refers to rotating joints in the opposite direction to its normal bending. In the real world this wouldn’t be physically possible without actually breaking a joint. In animation bending the joints in the opposite direction will add a lot of flexibility to a movement, and is typically used for a more cartoony style animation. Since you’re only breaking the joint for a frame or two when played back at full speed it isn’t noticeable. It is closely related to the principle of overlapping action, but applied to an entire chain, like an arm for instance.