Hi Ethan. Phase reversal is the reversal of polarity of the signal basically. It's only really important when there is more than one signal present. If you're listening to a single source or track, and reverse the phase you won't be able to hear any difference. But when it's mixed with multiple sources or tracks, then it changes everything.
So what is the use of reversing the phase? Ultimately it's up to your ears. Many engineers record snare drums with a top and bottom mic, and then reverse the phase on one and adjust the amplitudes of the signals relative to each other until it sounds the way they want. Remember that out of phase signals will cancel any frequencies they have in common at the same amplitude. This can be extremely useful. Let me illustrate:
I always prefer real rooms to digital ones. The studio I worked out of in Boston had a fantastic room for vocals. To record the ambience, I used two microphones in an omnidirectional pattern to pick up the room ambience of the singer. The problem is however there is always a significant amount of the singer's direct sound into the ambient mics (yes I realize I could've used the cardioid pattern and pointed the null at the singer, but I wanted the entire room bounce). If I recorded a mono track of the singer close mic'ed, and a stereo track of the ambient mics, when I brought the ambience up to the point where I liked it, there was too much of the singers direct sound from the ambient mics.
Reversing the phase of one of the ambient microphones can solve the problem. All things being equal (meaning the microphones have to be identical, the equalization etc.), you adjust the relative amplitude of the two microphone signals until you reduce the unwanted portion of the signal, and in this case the singer's voice. Then you have a stereo pair of tracks with nothing but the room ambience. You bring the mono track of the singers voice up in the mix, and then you can add as much of that ambience as you want and it doesn't cause any more center channel buildup, midrange smear, or just too much vocal. In most cases, I was able to obtain greater than a 60 dB reduction of the singer's voice and the ambient stereo pair.
Another good example is for acoustic guitarists that like to sing and record vocal and guitar at the same time. Trying to get separation between voice and guitar can drive you nuts. Once again, phase reverse can save the day. Put a microphone on the guitar. And then put another identical microphone in the air over the singer's head, but at the same distance from the singer's mouth as the guitar mic is. Reverse the phase on the overhead mic, and adjust the amplitude until you cancel out the singers voice.
You can make a noise canceling microphone out of any pair of identical microphones back to back, by reversing the phase of one of them. Signals that reach the microphone with equal amplitudes will be canceled. Any signal that's closer to one mic than the other, will make it through. this is exactly how mobile phones operate. Your mouth is always closer to the microphone on the bottom. But the car honking, the dog barking, the bus going by etc., all reach both microphones with equal amplitude, and are therefore, cancelled.
By all means, experiment and play around with phase reversal. Mastering the use of phase reversal can save the day!