In the field of Physics, Destructive Interference usually refers to the Interference of waves. Destructive Interference basically refers to the tendency of two opposite waves cancelling each other out. Sound waves are a good example, and you can see Destructive Interference in action if you have a tuning fork around.

Basically, when you whack the fork, the noise coming off the flat faces of the two prongs is much louder then the noise coming from the corners of them.

I'm not entirely sure how this works, because I came really close to failing physics. But I've seen (or rather heard) it.

This is actually being used (well, prototyped right now) in really new cars - basically, you have large speakers under the seats, and then microphones pick up noise coming into the car. The speakers then generate the opposite sound wave, and the two cancel each other out for a totally silent trip.

The only other thing I recall is that my teacher said it should be possible for airplanes to mask themselves from radar with destructive interference like this. Radar as mostly based on echoing sound waves, so if the plane had a radar detector that identified the frequency the radar was using, it could generate the opposite wave and cancel the radar beam out as it comes towards it. I guess the receiver would still get a blip for a second, but it would at least distort it after that.