When you gotta go and there is a someone in the bathroom. And you can't leave one on the floor because you don't want to clean it out of the carpet. You have to take a dump in your hand and flush it when its your turn. Most often used in large crowds when you can get away to poop but still want to be polite or when its easier to warsh poop off your hands then the floor.
"They had new carpet and I had to shit...only choice was drop a hand dump. Easier to warsh your hands then shampoo the carpet ya know?"