D3 is an inter-dimensional being that supervises 3-dimensional space in the Tenchi Muyo! world, including the universe that the show takes place in. He seems to take the appearance of a bearded humanoid man, projected from a large ovoid crystal.
It is not known to what extent D3 (or the other dimensional stewards) exercises free will, or if he is an automation. When he asks Tokimi "what to do with Dr. Clay," she responds with "I believe this dimension is under your jurisdiction," indicating that he not only has some authority to take action without consulting Lady Tokimi, but that she expects him to do so.
He doesn't appear to have a direct link with Tokimi, as he interacts with her using normal spoken language.
22 different Dimensional Stewards or "Ds" have been shown in total, with each ruling over an ascending Dimensional space. D4 has jurisdiction over 4-dimensional space, D5 rules over 5-dimensional space, and so onwards.