ColorFunction is an option for various graphics functions which specifies a function to apply to values to determine the color to use for a particular , region.
ColorFunction is an option for Plot3D, ListPlot3D, DensityPlot, ContourPlot, Raster and related functions.
With the default setting ColorFunctionScaling -> True, the arguments provided for the function specified by ColorFunction are always scaled to be in the range 0 to 1.
With ColorFunctionScaling -> False original unscaled values are used.
The function specified by ColorFunction must return a CMYKColor, GrayLevel, Hue or RGBColor directive.
ColorFunction -> Automatic yields a range of gray levels.
ColorFunction -> Hue yields a range of colors.
In three-dimensional graphics, ColorFunction is used only with the option setting Lighting -> False.
See The Mathematica Book: Section 1.9.6, Section 1.9.6, Section 1.9.7, Section 2.9.2 and Section 2.9.7.
See also: ColorFunctionScaling, Lighting, ColorOutput.