The Inverse Square Law is one of those things you learn about at college and then promptly forget - it doesn't after all have a terribly exciting ring to it.
If you use any kind of artificial lighting in your photography though, knowing how the inverse square law works is important.
So, what is it? The Inverse Square Law states that the intensity of a light source falling on a given subject is inversely proportional to the square of its distance from that subject. Or, in other words, if you double the distance of your light source from your subject, it will decrease by two stops; halve the distance and it will increase by two stops. Basically, as light travels away from its source, it starts to spread; as it spreads, it has to illuminate a larger and larger surface area, which means that its intensity decreases the further it has to travel.
Therefore, if your light source is positioned 1 metre away from your subject and gives a light reading of f11, and you then move it 2 metres away, the reading will now only be f5.6; by the time the light strikes the subject, it has spread out and has to illuminate four times the surface area that it would have to at its original "correct" distance of 1 metre - this equates to a loss of two stops of light. If, on the other hand, you halve the distance of the light from the subject by moving it half a metre away, the effect will be to increase its intensity by 2 full stops, from f11 to f 22.
This is the reason why if you use flash photography at say a party, and are photographing a group of people, whilst they will be correctly lit, the background will look much darker; by the time the light has travelled beyond the group, it has spread over a wider area and is therefore much weaker.
Similarly, imagine that you're photographing a large family group in a studio. If you position your light too far to the side, those people nearest to it will be lit more brightly than those who are furthest away.