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Dithering is the intentional use of noise (random sounds) to reduce the error of compression.

Example below:

Figure 1. Original photo; note the smoothness in the detail.  
Figure 2. Original image using the web-safe color palette with no dithering applied. Note the large flat areas and loss of detail.  
Figure 3. Original image using the web-safe color palette with Floyd–Steinberg dithering. Note that even though the same palette is used, the application of dithering gives a better representation of the original.  
Figure 4. Here, the original has been reduced to a 256-color optimized palette with Floyd–Steinberg dithering applied. The use of an optimized palette, rather than a fixed palette, allows the result to better represent the colors in the original image.  
Figure 5. Depth is reduced to a 16-color optimized palette in this image, with no dithering. Colors appear muted, and color banding is pronounced.  
Figure 6. This image also uses the 16-color optimized palette, but the use of dithering helps to reduce banding.