Accuphase C-200 "COMP" button - What does it do?

To add to the above:

Hearing acuity is subject to (if I remember correctly) the Fletcher-Munson Law. This is a measure of the reduction in hearing sensitivity to the high and low frequency extremes as the volume goes down.

According to anthropologists, the reason for this has to do with survival. i.e., predators produce mostly mid-range (crunching leaves, heavy breathing, etc.) and so by accentuating your sensitivity to the midrange at low levels (like at night for instance) you have a better chance of getting away before you get eaten.

For a similar reason, our visual sensitivity shifts to blue in low light at night (the color of moonlight.)

In the old days, those loudness circuits were often called loudness compensation.

It 'compensates' for the drop off of hearing in frequency extremes when the volume is lowered.
Unfortunately the compensation is a fixed one (probably about 20db at 20Hz and 4db at 16kHz) and not much use for accurate compensation.
Nakamichi and Yamaha had variable compensation controls on their pre-amps of the '70s, which compensated by reducing the volume at the mid frequencies only, thus being a more accurate compensation from the normal (flat) volume level.
Bob P.