The ratio of the power of the fundamental frequency at the output of a device versus the total power of all the harmonics in the frequency band at the output of the device. Basically, all electronic audio devices introduce some distortion to audio passed through them. The simplest form of this distortion is the addition of harmonics to the outputted signal. THD represents the sum of all the harmonics added by a device as a percentage of the level of the signal being measured. The closer THD is to zero, the more “transparent” a device should sound (all other things being equal, which they never are…).
Various devices contribute differing types of harmonic content to a signal, this is part of what can give them their distinctive sounds. For example, tubes add different harmonics than transistors, different circuit designs emphasize different harmonics, etc. When engineers talk about the “sound” of a piece of equipment, this is a part of what they are referring to.