Light propagates out from its source in all directions. The light passing through a unit square that is one unit from the source will pass through a square that is four times as large when it is two units from the source. This means that the light gets 1/4 dimmer per unit area. We say that light "goes as" 1/r2.
This plot shows the 1/r2function. Notice that the light falls off very rapidly at first, but then at long distances, the signal tapers off much more gradually. The image below of light propagating out through fog illustrates this property.