The first thing someone will tell you is that you are actually reversing the polarity, not phase. But enough people call it phase that everyone knows what you are talking about.
The textbook example of when, where and why about phase reversal is double micing a snare drum.
A snare drum will often be miced from the top and bottom. One mic is pointing down and the other pointing up.
When you hit the drum, the stick pushes the head down. Away from the top mic. Of course, it's also pushing the head towards the bottom mic.
The two mics will see somewhat the same signal, just in two different directions. When you mix them together, the low end cancels out and the snare sounds thin.
If you reverse the polarity of the bottom mic, the two signals are now going the same direction and are working together. It no longer cancels out all the low end.
Some mixers and mic preamps have a phase switch, but all DAWs have a utility to do this. It might be called "invert" "phase reverse" or something like that.
Another obvious time to have one mics polarity flipped is when you have a mic on the front and back of a combo amp. You would need to flip the polarity of one of the mics for them to work together.
