The Fog On/Off button does what is says.
Nice turn on and off a pixel based computation method which is suppose to give better results.
Color ... brings up the fog color editor. This color editor is shared by the Fog panel and the camera panel for the background color. Using the two color patches of this color editor, one can use the same color for the background and the fog creating a depth-cueing effect.
Fog with linear increase has two parameters Start and End defining at which distance from the viewer the fog starts to blend into the color and at which the distance the object is completely invisible because of the fog.
The exponential and exponential squared increase of fog use both the density parameter.