the phase correlation meter is a means to analyse how similar (or opposed) frequencies of the left channel are in respect to the right, and at the same time the other way round. +1 means both sides identical, resulting in twice the amplitude when summed together. -1 means they are completely inverted from each other, resulting in some strange very stereo sound but also in silence when both channels are summed. zero point is neutral, so when summed the amplitude will be the same as the mean of both stereo channels.
A pure mono sound would always be +1. Inverting one stereo channel of a mono sound -1 (the gainer device can invert either left, right, or both). The stereo expander can reduce width to mono mix, if you use l+r mix mode you will see the effect of the correlation in the (mono) result, i.e. a bass totally out of phase would result in silence. You can also put filters on the master channel to analyse specific frequency ranges for their correllation.
Having out of phase sounds will mean they will sound weird on headphones (though it can be an interesting experience, only parts of sound out of phase like with reverbs can sound very...wiiiiiiide), or when playback via speakers the frequencies can sound with a different balance depending on the position you have relative to the speakers. Also you should consider your music being converted to mono at some occasions, i.e. a big mono soundsystem in a club, a mono playback smartphone, a subwoofer that will sum left/right for bass frequencies (some sub setups also seem to choose either left or right for the sub).
Theres lots of things to consider when it comes to phase correlation/stereo width, its black magic. Every stereo effect and stereo layerings etc. will affect it in different, not always perfectly controllable ways, so if you want to be anal about the few dbs to be gained by correlation vs width games, you have to watch your sound design and mix business closely for possible phase problems. It is common to keep at least the bass in mono (below 100-200 hz - correlation near +1), or at least almost completely mono, to make sure it will always have full power, and also as stereo bass isn't useful anyways, only a bit weird on headphones. Some people mix/eq/balance their sounds with a mono mix on master completely in mono (just put stereo expander on master channel), so their balance of stereo sounds will work better regardless of the angle the listener has to the speakers.