The super short answer is conservation of energy. Now relook at the linked equation.
By conservation of energy, are you referring to the law the a surface cannot reflect more light than it absorbs?
1st term: Light being emitted from the surface that reaches the eye.
2nd term: Sum up all the light hitting the surface that reflects to the eye. It's a product of terms to get a how much of that part.
If the light is hitting a surface significantly larger than it's wavelength, then the surface can be modeled as a plane. The hemisphere is everything outside of the material.