Self explanatory, most likely would be an insight upgrade unlocked after purchasing the sacrifice statue insight.
Hero Statue: upon interacting, it will give you a quest you can complete that expires when you beat the current floor. These can range from killing a certain amount of enemies to spending an amount of money to even killing the mad merchant. If you complete the quest, you get an additional reward at the next rest area. You can view your quest by looking at your off hand like a watch.
Lovers Statue: upon interacting, gives you a "keystone" item you can store in your wrist pockets. Somewhere in the dungeon is another lovers statue, giving the keystone to this other statue grants a lovely reward. Only 1 set can appear per loop.
Statue Mimic: attacks you when you try to interact with it, but can be calmed down if you approach it with food. Grants goodies when fed and even relics if you feed it enough or give it high quality food.
I have plenty more ideas but I need to stop making huge suggestions so I'll end here.