Sphere Mapping is an environment mapping, or reflection mapping technique, that simulates environment reflections on an object's surface, using a texture map.
The texture map contains an image (light probe) of the surrounding environment reflected on a perfect mirror ball and captured, using an orthographic projection.
Such an image could also be generated during the rendering using a fish eye camera model.
An example of a light probe image and a scene using this image as environment map.
For each pixel on the surface the reflected direction from the object to the environment (the reflection vector) is used to look up a reflection color in the environment map.
This color is then added to the final shading.
The idea of the sphere mapping shader is to produce two color values for each pixel, the diffuse lighting color and the reflection color, and to combine these into the final shading color.
grace_probe.png light probe
Randi J. Rost, OpenGL Shading Language, Second Edition, Addison Wesley Professional, 2006
Udo Bischof , Environment Mapping, BTU-Cottbus, 2006