When a joint bends, the skin can "collide." Without collision detection, it can overlap unrealistically. This is especially likely when one or both of the links have bulges. The joint intersection controls can detect skin collisions and correct overlap by creasing the skin.
By default, Physique draws a crease plane that bisects the joint and prevents vértices from each link from crossing the crease plane. The result can be a somewhat unnatural flattening of the bulges along the plane. Physique therefore provides controls that let you modify the effect of the crease plane.