The Dark Kingdom is the realm of Queen Beryl and origin of the youma. The reason for the existence of the Dark Kingdom is reviving the evil goddess Metallia. Her slumbering form is somewhere in this realm, most likely in is centre and directly underneath Queen Beryls throne room.
The entrance to the Dark Kingdom is apparently located at the North Pole of Sailor Moons World. It is not clear whether it is located there under the ice or if it really is its own dimension and only connected to the World there.
The Kingdom is nominally governed by Queen Beryl with her four dark generals, Jadeite, Nephrite, Zoisite and Kunzite, directly under her. Those four chose the youma for their assigned missions themselves, but are otherwise mostly left to their own devices.