Please Help Me Understrand "Phase" Control

I have a "phase" button on the remote for my 2 channel integrated amp.  I have not cross wired the speakers so I assume that they are in phase with each other.  When I push the button to change "phase" on the amp, a signal light comes on the front panel so I know that it is either this or that, and I assume no light is the default position. It is on or off, not variable. There is no explanation of this function in the operator's manual. When the light is on, the sound is noticeably better;  a bit crisper both in the highs and in the sound stage separation.  So, what is happening when I change "phase" on the amp?
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Absolute Polarity.

Here are a couple of good articles for you to read on the subject.

Dave: You could quite clearly hear the difference. Your favorite test of absolute polarity is trumpet, correct?

Stan: It’s certainly, for me, the easiest; any instrument that produces a sawtooth or highly

non-symmetrical waveform will work. And the trumpet [or trombone] is so easy because your hearing acuity is highest in the mid band, which is where these sounds live. I remember one time helping a friend of mine here in town. Tommy Pearl has a band here called The Burners, and it’s basically like a Chicago group. It’s a rock band with brass [trombones and trumpets] and saxophones in it. Tommy plays very good trumpet. He had this sound system that was really quite good and I remember one time I was helping him get set up at the Officer’s Club, and he was playing his trumpet. Every time he played his solo into one particular mic (pinching his nose) "it just sounded like this." And he was having the guys run around back stage trying things with EQ and gain structure and everything else. And he couldn’t get that really bad sound out. He took a break and he came down to where I was sitting; we were talkin’ and I said, "Tommy, I think you’ve got a polarity inversion in that one cable." And he said, "Yeah, ’ya think so? Would that make a difference?" And I said, "Yeah, you can you blow on your trumpet, and the wave form is a sawtooth wave. You’ve got almost nothing here on the zero volts line and then you’ve got these big spikes that go up. But they don’t go down below the zero-line. They just look like the dorsal fins on a dinosaur, ’ya know." [Stan now knows that real dinosaurs, as opposed to cartoon dinosaurs, didn’t have dorsal fins, thanks to his friend Robert. Even the dimetrodon had but one "sail" on its prodigious back...]

"Now," I said to Tommy, "if you can imagine yourself suckin’ on your trumpet to produce the polarity inversion of that, the negative going, that’s what coming out of the loudspeaker." (Pinching his nose again) "It sounded really bad!" So he put in another cable and, "Wow-wee." It was there. Just ’ya know, like Clark Johnsen’d say, "the difference between night and day." And yes, it was, it absolutely was. It’s something that literally everybody in that band was able to hear, whether he was the drummer, or the keyboardist, or anybody. And they were behind the loudspeaker system! Because the loudspeaker system is along the front of the stage and they’re all behind it, they’re only hearin’ the back side radiation, and they could still hear the difference!

Following are 4 jpegs in a group for you entitled "Dick’s Trumpet"

Elizabeth nailed it. +1
The phase switch is the equivalent of swapping the red and black speaker terminals on both speakers at the same time.

It's use is controversial, as recordings, preamps, amps and DACs may or may not output in correct phase, and some listeners appear to be much more sensitive to this than others.
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