Phase is the relationship of two signals to each other - so if you have two identical signals (and sound is a wave form of energy) and move one of them forward a touch in time, they become out of phase, and this manifiests itself in (usually) unpleasant audio artifacts.
Think phaser effect pedal for a guitar... does exactly that - fine if that's what you want, but to be avoided when putting together multitrack music.
So you'd get this problem when using two different mics on a single source (say an acoustic guitar) - now the signals won't be identical as you're using two different mics in different positions, but they'll be close enough to potentially cause a phase issue.
To avoid this you can invert the polarity of one of your signals - usually in your software / recorder. Phase isn't inverted. If someone's talking about inverting something's phase then they don't know what they're talking about. Polarity is inverted, not phase. This turns the wave form upside down and (usually) eliminates the problem.
That's the short guide - do some reading around here and you'll learn lots more.