dude, basically sound travels in waves, just like the ocean, only the waves are much smaller and closer together. they actually travel, just like waves in the ocean, they move from the source of a sound to the object that is hearing the sound (and generally in many other directions as well). best example is a raindrop in an otherwise still puddle of water. raindrop is source of sound, the waves spreading out circularly from the drop are the soundwaves, and if your foot is stuck in the puddle somwhere a foot or so (for example) from the drop of water, your foot is in this case the object that is "hearing" the sound waves that originated from the drop of water.
Soooo, what happens if you have two drops of water land simultaneously 10 inches apart in the otherwise still puddle of water? the waves travelling away from the two drops combine into a combined wave that is more complex than the original simple and predictable wave. In audio this is how two or more sounds are able to be heard as distinct sounds by the listener even though the two sounds are sharing the same air to travel to the listener. BUT, what happens to the waves that aim directly at each other from the two drops, the waves directly between the two drops?
If the two drops are identical (very unlikely in water, much more likely in pro audio for mono sources coming from two speakers simultaneously), then the waves will both arrive at the listener identically and add together to provide a very full picture of what the drops sound like. If one drop however hit the puddle a half second before the other drop, then the waves will be "out of phase" with each other, or out of sync which is a decent analogy, and the "listener" will have the waves push back and forth from either side unevenly, out of sync, and the listener won't get a full loud and clear picture of the total summed sound of the otherwise identical drops of water.
They hit each other and cancel out most of their travel, and while some of the water from each wave continues on towards the other drop, some of the water actually stops moving dead in it's tracks because it hit the first wave. So if you were "listening" between the two drops, you'd not hear either drops' sound accurately, there would be parts of the sound that were "cancelled out" by each other's wave, and other parts that still made it through.
This is scientifically complete crap hahaha, water waves are quite different from soundwaves in reality. But as an example case it does get the point across. So if you have a pair of speakers and you reverse the wiring of one of them (+ to - and - to +), and you play a mono sound source and sit evenly between them, especially if it's a very bassy sounding tone, you will hear only part of the picture. If you put the speakers back in phase, you'll hear the full picture. it'll be warmer, richer, less "wierd" sounding, and won't have any artifical and unexpected stereo effect, it'll sit in the middle of your head where it should be if it's mono. If you switch the phase of BOTH speakers (so both are wired + to - and - to +, or gold to silver and silver to gold, red to black and black to red, whatever), your speakers will once again be back in phase with each other and everything will be fine. it doesn't matter if everything's one way or the other, but everything must be the same is the point, one speaker can't be different (out of phase) or you'll have problems.
Now for your mic phase question, the same thing goes, but it's a little tougher to know when to use a phase switch. Mics are the listener in this case, and if you have one mic you have no problems. if you have two mics, otherwise identical, and you are recording one source with them (like a piano is a good example, drums and guitar aren't quite as obvious to hear phase problems for beginners but still very important to know about), your mics must be in phase with each other. Doesn't matter if they're both normal or both reversed phase (whcih just reverses the wiring like in my speaker examples above), they must be the SAME or you'll get phasing issues that sound just like the speaker phasing issues above.
When it gets complicated is in multimic setups or setups with mics from different manufacturers (or even different models by same manufacturer). If you have 2 identical mics (or more) on an instrument you are probably doing it to get either a stereo effect or to cover more of the instrument (literally) with mics. piano = high strings and low strings. guitar = neck and soundhole. drums = left overhead and right overhead and sometimes a 3rd room mic (many feet in front of the kit for example). the positioning of the mics means that even if wired in phase and the same mics, being far apart will make sound travel to each mic at different times from teh same sources, like the hihat will hit the mic closest to it before it hits the mic further from it. So some sounds will be in phase, others will be out of phase. After learning the basics of how far apart you must put mics to avoid extreme phase problems (well covered info all around the web), you must also just use your ears to make sure it sounds clear and full, not "phasey". If it does sound phasey, try reversing ONE of the mics' polarity and see if it helps everything, it might help one situation and make another worse, or might fix everything, or might not be the problem at all. But that's when you start to experiment.
Also, mics from different companies or different models sometimes are wired in opposite phase to one another. So using a shure and a sennheiser together for drum overheads might not be as easy as it seems (not to mention just being wierd, but it's only an example). Same thing, you have to listen and experiment. Shure and sennheiser mics in your guitar amp setting might be very good, but this is an example where you will have to experiment and use your ears to decide which has a fuller sound. bass (lower) tones are the ones that get most obviously affected by phase problems by simply getting quieter in the bass area, higher tones tend to sound a bit hollow and sometimes (if you pan one mic to the right and the other to the left and listen with headphones) will create sort of a fake stereo effect that is exaggerated from how it will sound when you have them in phase. so play with phase reversing and see which is fuller.
Let me tell you though, as long as you follow standard rules for mic placement to avoid phasing when recording with 2 or more mics on one source instrument simultaneously, and you use the same mics for multimic recording (at least when appropriate), then you will probably not have to use the phase switch on your mic preamp very often. It "shouldn't" be the fix all for your problems, and should definitely not be used as an experimental device to make your mixes sound better or to change the tone of an instrument. It's just there so you can fix the problem with xyz microphone since you've learned from experience that xyz mic is generally out of phase with abc mic and you love using them together.
Long winded, hopefully helpful, and hopefully correct. Remember, this answer's targetted at the newbie, please don't flame me with scientific proof that I'm wrong, it's irrelevant, what IS relevant is whether or not this is helpful and good steering for a newbie. If anyone thinks the basic result will be wrong, then I'm happy to stand aside. But I think for a real newbie it's a good introduction.
But then I'm a wordy SOB sometimes... sorry if it's just a waste of space.
Cheers man
Don