First of all correlation meters only work when you are comparing your left and right signals of your stereo field. At best don't even look at them. This is just my opinion. I have the same opinion about frequency analyzers.dfegad
Anyway, the concept is easy: You have two signals from the same sound source, for example 2 mics on a guitar box at equal or different distances from the source. Set the volume of both signals to about the same level. Flip the phase on one an and it will either sound a) better or b) worse or c) little to no change in which case there is probably something wrong, like being at a 90 degree phase in which case you should probably just choose one of the 2 signals to be used. Same with say overhead mics and the snare top mic. Solo them both, flip the phase of the snare mic. Does it sound bigger, smaller, or no difference? Might not be a great example because if your Overheads are not in phase with each other than you are pretty much screwed. Then you might have to do some track nudging in which case it gets ugly and is no fun if you are mixing a complete album and always have to remember to do this on each song(been there). Other things to check are like the phase correlation between a drum room mono or stereo pair with the overheads or rooms far and rooms near. There are so many things to get wrong in the recording process it's unbelievable really. These days I'm doing more "fixing" than mixing but what the hell, I'm getting paid for my time.
This concept also works when you are using, say, 3 mics on one guitar cabinet. Match 2 signals and when they fit match the 3rd to the pair. And check again 3 to 2 and 3 to 1 as well. It can get dirty.
Back to the topic though, you can also use this concept to make interesting eqing - like mid scooping. Say you have a signal that is rather linear (seems to cover the full spectrum) and one that has a lot of midrange, you can add this signal and, if it's in phase, reverse the phase so that the similar frequencies cancel out thus resulting in a "scoop". Can indeed be very interesting but not exactly my favorite way to make sounds. But worth a try!
There are simply so many things that can be done with phase tricks but you need to first know when it's doing something undesirable before you try to implement it as a "trick".
I had a mix once where the overheads were out of phase with each other and, once I got them in phase, the snare needed to be flip at which point I realized the kick drum was at about 90 phase and made it sound like poop. I ended up triggering it with a kick drum sound that was so far away from the original that nothing could go wrong. Not fun.