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In many recordings and in many components, polarity gets reversed. The button provides a way of correcting this.
So, what is polarity? Musical waves have both positive and negative parts. The positive part of a wave corresponds with an increase in air pressure (or compression, not to be confused with data compression like mp3s use or with dynamic compression used to make records louder - this is compression of the air). The negative part corresponds with a decrease in air pressure (or rarefaction, the opposite of compression).
One key thing to understand about music, that differs from most test signals, is that the waves are asymmetrical. The positive and negative parts are not mirrors of each other. This can be easily seen in any musical waveform, like the type often posted in threads on this forum.
When polarity is reversed by a component or some element in the recording chain, the positive and negative parts of the wave are switched. A compression wave becomes a rarefaction and vice versa. What does this mean for music? (Clark Johnsen wrote an excellent book on just this, called "The Wood Effect".) As with anything in audio, there is much debate and some folks consider inverted polarity inaudible. In my experience, while the ease (or difficulty) with which it can be heard varies from recording to recording, when polarity is reversed, there is a "thin" quality to the timbre of many instruments and an indeterminacy of focus, imaging and soundstaging.
A polarity inversion switch works the same way as reversing the + and - connections on "both" speakers. (This is different from each speaker being wired with different polarity. That is much easier to hear as most bass goes away and images that should appear in the center will seem to be "everywhere and nowhere" at the same time.) The advantage of the button is you can make the change immediately.
I would suggest trying the button with different recordings and seeing if you can notice a difference. (This assumes your system is properly set up to get the best out of it.)
The most recent experience I've had with polarity issues was on the new release of "Revolver". After hearing a thin, somewhat "phasey" sound, I decided to compare waveforms with the CD from '87 ("Taxman" is a good example). These clearly show the two different versions are "upside down" from each other. Reversing the polarity on the new one removed the thin, phasey sound I was hearing, giving it more solidity and focus.