Phase inversion is a useful control under some circumstances and for some systems.
In essence what it does is reverse the polarity of the generated pressure wave from the drivers so that when a kick drum is initially struck, the re-created pressure wave is actually positive and not negative.
The ear can distinguish the differences between a positive vs. negative pressure wave when musical instruments are being played.
Bass is where I hear the greatest benefit from use of this control, in that the bass response is enhanced and extended to lower frequencies, assuming of course the track has those frequencies to begin with AND the system is capable of delivering these lower frequencies.
But all sources of sound (vocals, instruments etc.) will respond to the proper absolute system phase, but these changes are even more subtle and can take considerable training/calibration in order to hear them.
Overall though I consider the ability to change the absolute phase of the signal a 'must have' feature, so much so that I have added a data field into Media Center devoted to the absolute phase for each track I listen to.
And granted for some tracks it doesn't seem to make any difference, one way or the other, but for other tracks having the deep rumble of subsonic bass present as well as the increase in the leading edge dynamic impact of every instrument, even for instruments such as piccolo's, and all tied into the music, is most gratifying.
So getting all this dialed in can result a most satisfying and delightful experience.
And the ability to hear and feel this degree of bass is MUCH more discernible on HP's than speakers, that is unless you have WAY more $$$$$$$$$$ than ¢'s, and even then it's often hit or miss if you can actually get speakers to re-produce true musical bass down to 20Hz and below.
JJ