Atmospheric Perspective is a way to control spatial relationships in an image. It is another strategy to give the illusion of virtual space within a two-dimensional image.
In Black and White or colour photography it differs from the other controls we can use(e.g. depth of field, linear perspective etc). Black and white the effect is primarily the reduction of contrast as the distance between the viewer and what is seen increases. The atmosphere thickens with distance. Atmospheric perspective is a way to enhance this illusion.
In colour Photography the use of the use of warm colours tend to bring objects closer to the viewer and cool colours tend to make objects fall back.
Photography with film requires the shooter to choose his subjects carefully if he wants to capture atmospheric perspective. There is some darkroom manipulation possible such as dodging or etching.
The digital photographer is very fortunate because there are so many Photoshop tools to manipulate the background. Hue (colour), saturation (intensity) and brightness (tone) can be controlled independently.