Basically, there are two methods for calculating the final image in the render. Montecarlo is an algorithm that calculates the trajectory of the rays casted to get the correct shading. This method is tedious and filled with calculations, but totally accurate. The irradiance caching method is interpolated, so you get faster calculations, but they are lesser accurate.
The montecarlo (MC) method involves a complete calculation, with no interpolation at all. It works on a brute force calculation.
Let's get back to the box scene but with a light in the ceiling. The polygon acting as a light is just a material with the Luminous Intensity field enabled (see Chapter 3, Texturing and Materials for reference). To illustrate the MC method, we will disable Irradiance Caching and see what happens:
The MC method assigns a number of rays to the light source and then casts them from the light to the scene, just like in the real world. This is...