science - What is the inverse-square law, and how does it apply to lighting for photography?

I hear photographers talk about the inverse-square law, particularly with reference to lighting.

What is this law about, and most importantly, how is it applied to lighting for photography?

Answer

The law states:

If you double your distance from a light source, the amount of light reaching you drops to a quarter of what it was.

More generally:

If you multiply your distance from a light source by X, the amount of light reaching you will drop by a factor of X^2 (X squared)

As is often the case, Wikipedia explains this very nicely (with a nice graphic, too).

Use for photographers

This means that you don't have to move very much relative to your light source in order to see a big change in the amount of light.

So, if you are lighting a subject with a strobe, you only have to move the strobe a little closer or further away to achieve a big difference in the amount of light reaching the subject.