Just so everyone's aware, the terms "Phase" and "Polarity" technically refer to different things. This post is talking about reversing the POLARITY of a mic. this is often (mistakenly) refered to as reversing the PHASE
PHASE has more to do with time, and the distance of multiple microphones from a single source.
For example, a transformer will shift the phase of a signal about 90 degrees. as do some passive crossover networks. EQ can also cause phase shifts. this mainly has to do with the time... certain frequencies will be slightly behind others... thus coloring the sound. this is sometimes good, sometimes bad.
or say you were micing up a drum kit... if you're using more than one mic, then you may encounter phase problems caused by different drums arriving at different mics at different times, and cancelling certain frequencies, causing COMB FILTERING.
there are many more detailed explanations on this forum, by people with much more technical knowledge than I.