Hunger is a property which increases the rate at which you burn nutrition by 50%. It is conferred exclusively by the ring of hunger - extrinsically from wearing it, and intrinsically from eating it.
Other properties, such as conflict, also cause an increased hunger rate, but this increase is handled separately from the hunger property, causing their effects to stack.
Slow digestion is independent from hunger, and they do not cancel each other out; if you have both properties at once, you will burn nutrition at 50% of the normal rate plus jewelry adjustments.
Extrinsic hunger is occasionally useful when you want to stop being satiated, in order to avoid dexterity penalties or eat more corpses. However, it is usually considered bad to have as an intrinsic, and a tinning kit is preferable for managing corpse consumption and nutrition.