From Dungeons of Dredmor Wiki
The Statue of Eyes is one of several distinctive objects, alongside the Mellow Altar
and the Monolith
, that are the focal point of certain quests given out by Inconsequentia
, Goddess of Pointless Sidequests. If clicked on without a quest item selected a message appears saying "The eyeball shrine stares at you with millions of creepy little eyeballs."