Presumably, a creature that prefers to eat stone
s, or other mineral
s. Probably also applies to creatures that will eat gem
s or sculpture
s as well.
In NetHack, polymorphing into a petrivore allows you to eat boulders, rocks, flint stones ("Yabba dabba delicious!"), and any ring, wand, or other magical item made of stone with impunity. If you eat a magical item, you sometimes gain a corresponding intrinsic power. Another way to accomplish this is by casting the stone to flesh spell.
Actually, as of version 3.3, the above information is somewhat misleading. The majority of rings and wands cannot be eaten. It is much more useful for a player to polymorph into a metallivore.
Rings of slow digestion cannot be eaten, for obvious reasons.
NetHack petrivores include xorn, rock moles, and probably ochre jellies.