Zogre bones are bones obtained from killing zogres and skogres.
Zogre bones give 22.5 Prayer experience when buried, 78.7 Prayer experience when used on a gilded altar with both incense burners lit, and 90 Prayer experience when used with the Ectofuntus.
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