What does it mean?
Harmonics help shape timbre. Nonlinear processing can create new harmonics; the metallic components produced by ring modulation need not be integer multiples of the fundamental.
ExampleA 100 Hz fundamental can have harmonics at 200, 300, and 400 Hz.
How the meaning changes between controls
Guitar Synth
The Character control changes with the voice: Harmonics, Drawbars, Metal, Bow / body, or Brilliance. These labels do not mean every model has the same physical parameter.