At every point on it, there is some radiance that's a function of both direction and orientation. You look at it from somewhere. We do direct highly accurately, we call indirect things zero for now. This forms a simple enough physical approx that it's easy to implement. Consider a dA of the light area.
Reflectance is the ratio of light out to light in.
Pete's never seen a good argument as to where it comes from. Has seen proofs that it must be there, but no good intuitive argument. Figuring out an anaytic domain of integration is a problem due to shadowing. If there's something between x and x', the light gets blocked. A where x is a uniform random position on the Light.