Invert ?

While it is very common to call this "phase" inversion, calling it polarity inversion makes more sense to me but, that is a minor point. The first thing to be aware of is that not everyone is sensitive to "absolute" polarity inversion which is, both channels being inverted at the same time. I know a couple of people that say they don't hear any difference. There is also the not common issue of "relative" polarity inversion which is, just one channel being inverted, usually by an incorrectly connected speaker wire on one channel at either the amp or the speaker (red to black and black to red). I think that most people can hear that something is wrong when relative inversion exists in a given system. 

Paul's explanation is a bit on the technical side. Here's what I perceive when comparing correct polarity to incorrect polarity The sound with correct polarity will project outward toward the listener and there will be more space and air around the sounds and voices. Incorrect polarity will move the soundstage back a little and will flatten the soundstage as well. There will be less space and air around the sounds. In my experience the effects of correct/incorrect polarity will vary with speaker design in particular, speaker placement in the room, and all of the other variables with room dimensions, wall treatments, etc.

If you don't pick up on the differences at first, pay attention to how the bass sounds and also high sounds such as high hat cymbals as you try each switch position.

Yes, as yogiboy said, some recordings are polarity inverted.

@yogiboy  i watched the video. TY.  But  As Denzel Washington said in the movie Philadelphia “ Explain this to me like I’m a 2 yr old because there’s an element to this thing I can’t get through my thick head. 🤦‍♂️🤷‍♂️

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. 

@larryi Nice explanation.  Thanks!

@mwh777  +1. Great explanation

Pual Mc educated me decades ago, except he incorrectly calls Polarity Phase, which he admitted. I  first learned about it when I had Genesis Vs with powered sub, which had RC of volume and Polarity. I discovered the biggest offender was bass Polarity. If you're looking for a sub IMO, best is one with RC of Polarity. That said Polarity/phase on a remote preamp or integrated is very meaningful to my ears

hth