A Healstone was a feature that would heal your pets. All you had to do was walk up to the Healstone and activate it by correctly answering a question. It is said that Noot must activate it for you.
There are no more Healstones due to instant healing after each battle. As of the March 28th, 2018 update, finishing a battle will heal your HP, as Healstones were removed. The update has removed many other things too.