The indestructible teacup is an artifact used by ChocolateEevee, Frosti, and Pope. In Choco's and Frosti's cases, one of them will generally throw it at the other, assumed to be a reference to a youtube video or an iScribble inside joke. Pope, on the other hand, will place it on his head as a thinking cap, which usually prompts Frosti to throw pebbles at it.
It is known to be indestructible because it should break after barely missing Frosti or falling off of Pope's head, but does not. If one should attempt to throw it into Choco's all-destroying fireplace, it would cause an explosion that could engulf an entire continent, as Frosti suggests, or might even cause a universe-shattering paradox as theorized by Pope.