Zogre bones are bones obtained from killing zogres and skogres, which give 22.5 Prayer experience when buried, or 78.7 xp when offered at the Wilderness chaos altar or a Gilded altar with both burners lit. They can also be turned into zogre bonemeal which gives 90 xp when offered at the Ectofunctus.
If burying the zogre bones in Jiggig, there's a 1 in 4 chance to give no Prayer experience, and to instead spawn a skogre. The skogre will despawn after 5 minutes.
For an exhaustive list of all known sources for this item, see here