Relative phase is whether the left channel is in phase with the right. If the system is in correct relative phase, a mono bass signal will move the woofers in the same direction. If you've got that wrong, a mono signal will not be localized between the speakers, but will seem to come from all directions. You'll know when you've got that wrong. That's a onetime fix. If you have a recording that's out of relative phase, the person that did the last quality control check had a very bad day.
Absolute phase refers to how the original live performance compares regarding phase to how it's being reproduced on your system. For example, assume that a given wave front in the live performance consists of compression, rarefaction, compression, etc.. If your system is set for proper absolute phase for a recording of that performance, it will regenerate that "compression, rarefaction, compression, ..." wave series. If your system is set to the wrong absolute phase setting, it will generate a "rarefaction, compression, rarefaction, ..." wave series.
Unfortunately, as the sound is digested through all the steps of the recording and reproduction process, the end product that's input to your audio system may be either correct or inverted in absolute phase relative to the live performance.
The human ear does not respond symmetrically to compression versus rarefaction sound energy. It's actually slightly less sensitive to compression than rarefaction. Include the subject of just how the brain converts the nerve signals from those alternating pressure waves into our perception of the timbre of music, localizing sonic images in space, etc., and I have to refer you to Arthur C. Clarke's sentiment-- "any sufficiently advanced technology is indistinguishable from magic". Nonetheless, when you toggle the absolute phase setting of your system, changes in various qualities of the reproduction are audible.
Having the capability to switch absolute phase on your remote makes the correction of this issue trivial-- just switch between the "invert/normal" setting and let your ears/brain be the judge. It should just take a couple of seconds.
Regarding the question of whether this makes a difference in multimiked recordings, in my experience the difference is still clearly audible. Even with multimiked recordings, a decent engineer or producer should at least have all the inputs in phase. In my experience, multimiked recordings are definitely inferior to those using a very small number of microphones (e.g. the Decca "tree"). The most gross offender that I've heard is DG' awful "4D" recording technique where they used lots of microphones to spotlight various instruments and then use mixing boards as a musical Cuisinart to mix the signals together. Even on those abominations, switching absolute phase is clearly audible, though the correct absolute phase setting won't turn a DG 4D recording into a classic Decca one.