Definition: Dithering scatters different colored pixels in an image to make it appear as though there are intermediate colors in images with a limited color palette. (Continued below...)
Your operating system will automatically dither images when your display settings are set to 256 colors or less. Dithering is often used to reduce banding in GIFs with graduated color transitions. Most software provides options that let you control the appearance of the scattered pixels; for example, the dithering can be a rigid pattern, random noise, or diffusion. Keep in mind that dithering often increases the file size of an image, but in many cases the improved appearance is worth the trade-off. Below are several examples of different types of dithering. The last example is is not dithered. Notice the changes in file size for the various types of dithering.
Diffusion dithering, 4 color GIF, 2.00 KB
Pattern dithering, 4 color GIF, 1.31 KB
Noise dithering, 4 color GIF, 2.36 KB
No dithering, 256 color GIF, 6.00 KB
Optimizing Animated GIFs
Includes file size comparisons of dithered and non-dithered images.
Elsewhere on the Web:
The pros and cons of dithering and when and when not to use dithering in your images.
Dithering & Decreasing Color Depth in Paint Shop Pro
A tutorial from psptips.com.