When an instrument first emits a sound, the wave starts as a positive pressure that rises and falls followed by a negative pressure (lower than the initial static pressure before the sound wave arrived). Ideally, the speaker should follow the same pattern as the original sound wave. But, in the many steps of the recording and playback process, the correct order of compress first (or vice versa) followed by negative pressure may be reversed. Since, almost all recordings involve multiple microphones and line feeds, any one such feed could be inverted, so the effects of inverting polarity in your linestage may be very subtle and one position may not clearly be superior to another even when differences can be heard.
Because your gear itself can be inverting phase, you may not know whether or not your system is generally inverting phase. The effect of such inversion is subtle enough that it is not easy to make a reliable comparison by switching around the speaker connection, and a more instantaneous comparison via an inversion switch is helpful.
Why don’t most better gear offer this switch? This capability involves adding another active stage that theoretically degrades the signal.