1) To have an extreme urge to defecate, so much so that the feces is already spreading the anus and a portion of it is beginning to stick out. So called because it resembles a turtle poking its head out of its shell.
2) The portion of a long log of shit that protrudes above the water in a toilet. Since it is above the water, it can be smelled. So called because it resembles a turtle poking its head out of the water.
1) May I use your bathroom? It's urgent, I have a turtle head poking out.
2) You may not want to go into the washroom for a while: I just had a crap and there was a turtle head poking out; the smell is awful.