When we reduce the word-length or bit depth of an audio signal, such as when converting a 24-bit master to a 16-bit audio file for a CD we lose 8 bits worth of fidelity. This greatly increases the difference between the original audio signal and the resulting data (known as quantisation error) and audio files can sound harsh, reverb tails become ‘grainy’ and there is an increase in the noise floor.
The arises because losing the least significant 8 bits introduces a predictable level of quantisation error. However by adding very low level dither noise, a tiny ‘random’ signal, you remove the problem. The errors become unpredictable, smoothing over the truncation. The result is a marked reduction of distortion and retention of fidelity.
But a word of warning: dither should only be applied once, usually as the last stage in the production of a CD. And dithering for lossy formats is not considered necessary as the act of data compression largely removes the benefit of the process.