Firing a large weapon like a shotgun or rifle from your hip. Basically you just support the weapon with one hand hanging off to your side and pull the trigger and hope for the best. This generally gives you a real appreciation for how much these weapons really kick.

Well, emphasis on hope for the best should be made in sgtbaker's writeup. While shooting from the hip is an impressive idea (not unlike double shooting with two pistols), the rifles and shotguns out there have sights for a reason -- one should aim by looking through the sights!

Speaking of which, "Shooting from the hip" is a phrase used to describe a person (like a politician) talking impressively and quickly, but not always accurate.