As with many new arts, defining what “spectral music” is isn’t easy. Simply put, it’s a music which concerns itself with the evolution of sounds (or “sonority” or “timbre”) rather than with traditional notes, chords, counterpoint, etc. Timbres (flute vs piano vs chainsaw) are made out of fundamental tones and overtones: the manipulation of overtones seems to have been part of SM at the outset.

The image to the left shows the evolution of a sound in two-tenths of a second (horizontal axis). The vertical axis shows which frequencies are present in the sound at any time. These collections of frequencies, and how they change in time, are what give individual instruments (cello vs. trumpet) their unique character.
The result could compare to listening to water burbling in creeks or rivers … the ever-changing sound of ocean waves … wind among the rocks or branches of a stand of pines. The sound of an orchestra arriving at your ears is an amalgam of dozens of timbres at once; yet you can pick out notes played by a soloist.

A highly technical subject. This 47-page PDF is part of a dissertation. Another article called Acoustics, psychoacoustics and spectral music is shorter but also quite deep.