A distortion meter can automatically measure total harmonic distortion, or, essentially, the ratio of the sum of the powers of all the harmonic elements. In English, having less total harmonic distortion from a speaker enables a violin to sound like a violin and not another instrument or a distorted noise. A distortion meter allows you to measure the distortion from a signal source and adjust it accordingly.
A distortion meter allows you to remove distortion digitally from your source audio. It does this by calibrating your distortion to a test signal that you can input yourself.
Distortion meters can display your harmonics. Harmonics are sound waves representing the vibrating of a particular oscillator, such as a plucked guitar string or the human voice. With a distortion meter, you can see any amount of distortion in your harmonics and adjust them.