Harmonic distortion occurs when a system's output contains frequencies not present in the input. These are integer multiples: 2nd harmonic (one octave up), 3rd harmonic (octave + fifth), etc. Even-order harmonics (2nd, 4th, 6th) are perceived as warm and musical (tube amplifiers); odd-order harmonics (3rd, 5th, 7th) are perceived as harsh and edgy (solid-state clipping).
THD+N (Total Harmonic Distortion + Noise) measures all distortion products as a percentage. Below 0.1% THD is generally inaudible for music. But the SPECTRUM of distortion matters more than the total — 1% of 2nd harmonic may be pleasant while 0.1% of 7th harmonic may be objectionable.