You cancel the cooldown animation by going into the reload animation, then you cancel that by doing a melee attack. And then you shoot.
It allows you to shoot the shotgun like 30%-40% faster depending on if you're good or not. Its really NOT that useful except w/shotty standoffs where you both miss, or only get a partial hit and its like ZOMQ WHOEVER RELOADS FIRST IS GUNNA WIN!!! If they shotty cancel its like -_-' well that was dumb.
Its more annoying than practical, and really just makes people use shotgun sloppily.
Actually... It does have one practical use. Taking out a room full of people.