Phase describes where in it's cycle a periodic waveform is at any given time. The relationship in time of two or more waveforms with the same or harmonically related periods gives us a measurement of their phase difference. Phase cancellation occurs when two signals of the same frequency are out of phase with each other resulting in a net reduction in the overall level of the combined signal. If two identical signals are 100% or 180 degrees out of phase they will completely cancel one another if combined.Phase cancellation is handy if you want to, ie. extract vocal part from the song. You just need a track with vocal part and instrumental (dub) version of same track. If the signals are identical, you just need to invert phase of the instrumental version and every signal (except vocal) will be canceled.
But it's just one, pretty common usage - the video shows more interesting examples, usable for DJs and producers. It's helpful when building DJing effects, as it allows to utterly mutilate / phase / beat-repeat / delay / etc. the high frequencies of a track, without affecting the bass and kick in any way. One of the limitations of classic effects is that they apply to the entire audio stream, so they can make the kick messy or otherwise cause the energy of the track to drop. Isolating the bass and leaving it untouched avoids this problem entirely.
You can download the Ableton Rack shown in this video here
ps. the sound quality is not the best one but I find this video quite handy :)