Cannibalism is an invention that allows the player to loot more food from dead bodies. Cannibalism 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 love to fight enemies. It can be quite important when you're getting many swordsmen, since you will suffer a lot of damage while fighting other big tribes.
When cannibalism is bought, tribe members will cause dead bodies to drop one extra food from corpses, whether it's their own dead minion, a minion from another tribe, or barbarian. It will also affect dead bodies killed by other tribes or barbarians. Drops from minions are randomized, so in a situation where you would have gotten 0 food cannibalism gives you an extra, meaning that every time you loot a corpse, you get at least 1 food.
Any member in your tribe can use this invention to gain an extra food upon looting a dead body; there are no restrictions on that. When butchering a dead body, there are no visual differences other than more food popping out of the poor minion.