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"Comp (Compression): In CD mode, press to adjust the soft and loud passages together for a more consistent listening level. Press the COMP control until COMP ON is displayed."
That's straight out of the Owners Manual since I have no clue what it really does. I've seen it on my stereo a thousand times, but until you asked, I never even bothered to find out.
I can tell you what dynamic compression does on a home stereo and when you would use it. If you're listening or watching late at night and there may be people sleeping in the house, you turn on compression so that the bass isn't as prevalent. It squishes the peaks of the loudest waveforms so they aren't as loud.