The word Harmonics is clearly taken from Acoustics and we matches the fact that each component has a frequency which is an integer multiple of the fundamental (F, 2F, 3F, 4F....)
The amplitude of each term is lower for terms a higher number, so that while considering of order given signal (the the ensemble of the frequency components of a so-called SPECTRUM), it is not necessary to consider infinite harmonics since the amplitude (and importance) of these becomes quickly negligible practice a Fourier's analysis of a signal is never pushed beyond the 7th term, n while stopping at the 3rd is satisfactory for most applications.