I'll give it a shot.
Polarity and phase are different things, usually, in audio. Phase reversal is a misnomer. It should be called polarity reversal.
In this case, out of phase has to do with two audio signals from the same source, one of which is delayed in respect to the other. It can happen with more than two, as well, but two is easy to think about.
A common way for this to happen is two mics capturing the same source from different distances.
When the signals are played back, one of the signals is delayed in relation to the other, as it took longer to reach the farther microphone. The two signals are out of phase when played back together, in other words.
When the two out-of-phase signals are combined, some frequencies are cut and some are boosted, to different degrees. This results in what is called "comb filtering", as the peaks and dips in the combined response of two out of phase signals can resemble the teeth of a comb. It has a characteristic sound, and is used in guitar pedals and signal processors as part of the "phaser" effect. A "swooshy" hollow kind of sound.
Change the distance of one of the mics, different freqs boost and cancel.
Put the mics the same distance away from the source, no cancelling.
Polarity reversal is different, in audio. Plus and minus are reversed. There is no delay involved.
Example:
A signal goes from 0, up to 1, and back to zero.
If the polarity is reversed, the signal goes from 0, to -1, and then back up to zero.
Adding identical reversed polarity signals together results in no sound, in theory. The opposing signals cancel each other out at all points, as for every + value there is a - value at the same time.
This is what happens when you miswire one of a set of stereo speakers. It has the wrong polarity. The low end often disappears, as it is usually in both channels and cancels. Anything else that is in both channels will drop in volume as well. If your system is mono, most everything will disappear.
Another example is micing top and bottom of a snare drum at the same time. The polarity of one must be reversed. Striking the head of the drum results in one mic diaphragm moving one way, the other the opposite way. The two signals are of opposite polarity at the mics. One must be switched to prevent wideband cancellation of the signal on playback.
Now, put the two concepts together. Reversing the polarity of a microphone can help with phase issues by reversing the polarity of frequencies which are cancelling due to being out of phase. Other frequencies cancel, but the problem should be more obvious one way or the other. Polarity reversal (generally) moves a lot of comb filtering out of the range you are trying to fix. (hopefully)
Example:
Your overhead mics are at exactly the right height so that the snare drum sounds like crap when you listen to your snare and overhead tracks together. The snare sound is being affected due to phase issues.
Solutions:
Move the overheads, reverse the polarity of either the overheads or snare, or maybe even do both.