The property hunger increases the rate at which you burn nutrition by 50%. If you acquired it by wearing a ring of hunger, it is an extrinsic; if you acquire it by eating a ring of hunger, it is an intrinsic. Extrinsic hunger is occasionally useful when you want to eat a corpse before it spoils, for one benefit or another, but are satiated and thus might choke.
A ring of slow digestion does not affect the hunger property. For example, if you wear one in combination with a ring of hunger, regeneration, or conflict, you will hunger at about 1/2 the normal rate, as opposed to 1/20.