The material color is the reflection factor; they're the same thing. A material looks like a certain color because it reflects different fractions of R, G, and B light.
But you don't have separate R, G, and B photons (well, you could, but this isn't the way it's typically done); you just have a photon, and you must decide whether to reflect or absorb it. You must somehow condense three numbers, the RGB material color, down to one number, the probability for reflecting or absorbing.
A reasonable way to do this is to choose the max of the RGB components (although personally I would probably choose the weighted average by eye sensitivies to R, G, and B, rather than the max).
But when you reflect the photon it must pick up the material color. So you multiply the photon color by the material color. But now you've incorporated the material color twice - once to calculate the probability to reflect a photon, and once to modify the photon color. That's wrong, so you must compensate. You can do this by dividing the photon color by the probability. That way the photons still pick up the material color but the total amount of reflected light is correct.
In other words, you're splitting the material color into an overall intensity - which tells you the probability to reflect a photon - and the actual color part, which tells you how to change the color of a photon when it reflects. These two when multiplied together must give the original material color, so it follows that the "color part" = material color / probability.