Today's video can be viewed (here) and gives an excellent treatment of this subject.
There are various forms of "the" inverse square law. The one that interests photographers particularly relates the intensity of light arriving at a point to the distance from the light. Mathematically it is expressed as below:
Intensity ∝ 1/distance2
or even more basically as:
Intensity ∝ 1/(distance x distance)
where the squiggly character ( ∝) is the symbol for direct proportionality. Two different quantities are directly proportional to each other if one value divided by the other value always yields the same value. For example, the distance travelled by an object moving at a constant velocity is directly proportional to the time it has been travelling. A car moving at a constant velocity of 30 mph will cover 30 miles in 1 hour, 60 miles in 2 hours etc etc. 30 divided by 1 and 60 divided by 2 both yield a vale of 30.
Applying this to light intensity we see that comparing the light intensity at 1 and 2 metres from the light source, the light at 2 metres will be one quarter of the light at 1 meter. The light intensity is lower at the greater distance from the light as it is governed by an inverse relation (divided into 1), and the light intensity decreases by a factor of 4 for a doubling of the distance.
All your need to know as a practising photographer is that the light intensity falls off really quite quickly as the distance to the light increases. So keep your light source close to the model and a long way away from the background if you don't want to illuminate the background! Obvious really!