The frequency domain is nothing more than an alternative way to represent some signal. Nevertheless, it is of fundamental importance as it visualizes certain kinds of information that cannot be appreciated otherwise.
Signals in the frequency-domain are represented as functions of amplitude (vertical axis) versus frequency (horizontal axis). As such, a spectrum is fundamentally different from a waveform in that it represents how sound manifests in perceptual, rather than physical space. Indeed, spectra give no indication on how a signal would manifest in the physical world if translated to sound, yet they do accurately describe what the harmonic content of this sound would be. This should be of no surprise if we are familiar with the mechanics of hearing and particularly, of the physiology of the inner ear. Therein, a number of hearing cells inside the basilar membrane, each of which is sensitive to a particular frequency range, will fire neural spikes...