The Light path node allows you to make shaders do different things based on where the incoming light ray was before. When thinking about where "before" is, keep in mind that cycles is a backwards path-tracer.
The Ray Depth output of the light path node gives the number of bounces the ray went through before hitting the lamp (or whatever is using the shader).
So when tracing backwards from the camera to the lamp, surfaces which are directly illuminated (1 bounce away) will hit a lamp with a corresponding strength of 1:
Surfaces illuminated by indirect lighting (2 or more bounces before hitting a light source) will "see" a correspondingly stronger light source:
To see it in action:
As to why it appears "more realistic", I think this really just an artifact of the lamp being way too bright in the first example (it looks fine when the strength in the light falloff node is then set to 1). In fact the setup with the ray depth is less technically realistic, as explained above.
Normally the light falloff node is plugged into the strength, not the color. Then with the default strength of 100 it looks just fine: