The Demonstone slot is made available once you get to Level 1000, it will not show up on your equipment screen until then.
Demonstones can only be gained by completing quests for the Subterran race in the Eternal Plains realm, they are extremely powerful items that offer great new combat powers.
Known Demonstones
For more information on what powers these Demonstones grant I recommend going to the Library > Items menu and choosing the Demonstone slot.
Some demonstones may have not yet been found, as no one really knows where the Demonstones come from.
To use a Demonstone in combat you must first equip it, you may only use one Demon power in combat based on the Demonstone you have equipped. After equipping the Demonstone you should note a new button on the combat interface spell casting row, this button will activate your demon power. Once activated the power will run for the entire length of the fight with no way to shut it off.