Ratio between the amount of forward to backward scattering. With a positive value, more light is scattered from behind the object, with a negative value more light is scattered from in front of the object, relative to the observer.
With this example we have two lights, one in front, one behind our sphere. Both are very strong and the one behind is colored green, the one in front red. With Asymmetry set to 0.5, the light from the green light is scattered forward towards the observer, in this case the camera. When Asymmetry is set to -0.5 the light from the red light behind the camera is reflected toward the observer.