Dithering is a process designed to minimise the unwanted side effects of reducing an image or audio files word length (bit-depth). It is a process most often associated with reducing the word length of audio and image files.
It is often desirable or necessary to reduce bit depth. Here are a few scenarios ...
When you reduce bit-depth you lose quality. Dithering is a process which attempts to minimise this quality loss.
Audio dithering is a process whereby low level white noise (random sound) is introduced into the signal to help randomise quantisation errors. The effect of this is to turn the audible effects of quantisation errors from unpleasant distortion into a the more acceptable analogue noise.
Image / colour dithering is a process whereby a number of pixels of 2 differing colours are arranged in a pattern in order to simulate the effect of a third colour during image optimisation / conversion / "downsampling".