Any sound can be described as a recipe of frequencies, and the spectrum is that recipe read out at one instant. A kick’s energy piles up low with a click up top; a voice stacks harmonics above a fundamental; a cymbal spreads noise across everything high.
Audible frequencies run roughly 20 Hz to 20 kHz, and mixes distribute energy across that range deliberately, which is why spectrum analyzers sit on every mastering engineer’s screen.
For visuals, the spectrum is the raw material. Every audio-reactive system starts by asking where the energy is, usually via FFT, then maps regions of the spectrum to elements of the image.