Answer by E. Thompson:
A lot of it is what is called "sound design" in the post production process. The visual part is just a fake arm or leg that they "break" while hiding the real limb out of the shot or in the clothing. What really sells it is the sound design, which is the sound of the breaking and cracking that is added in the post production of the film. If you which a fight scene with the sound off, you will notice it is much less impressive and you may catch some mistakes because your attention is purely visual.
On a side note, there is bit of a flaw at the end of the Ip Man scene from above. You notice that after the fight his first two knuckles are bruised and bleeding. In Wing Chun Gong Fu the last three knuckles are the preferred striking surface to maximize vertical bone alignment and center line theory.