When you have to take a dump in a public restroom, but the toilet seat is too filthy so you have to hover over it and unleash.
Jaheen took a hovershit in a truckstop after eating a bean burrito.
Mainly applicable to women (intoxicated women) that hover because they don't want to sit on a nasty toilet and have to people very very badly. Sometimes, when a woman is in the position, pushing urine out with force, a little something else comes out. The desire to poo isn't even there when you go to the bathroom, but with all the muscle action, it is thrust out into the world.
Person A: "I just pissed and some poo came out!"
Person B: "Oh man! You just hover shit!!"