Butchery is an invention that allows the purchaser to loot more food from dead animals. Butchery has no requirements to buy, and thus can be bought early in the game. It can greatly help tribes that are low on food but do not want to risk mushrooms.
When butchery is bought, tribe members will cause dead animals to drop one extra food from animals they killed. Looting animals killed by other tribe that does not have butchery will not grant additional food.
Any member in your tribe can use this invention to gain an extra two food upon looting a dead rabbit; there are no restrictions on that. When butchering an animal, there are no visual differences other than more food popping out of the poor creature.