Non-existence is the state of not being there at all — or not being there in the place you are talking about. Philosophers use it for “this thing is not real”; ordinary English uses it more loosely for “there is none of this here.” You might talk about the non-existence of a bus at night, or of proof, or of a species in one country. The sister word nonexistent (often written non-existent) is the adjective: the bus is nonexistent. This noun is the “-ness” of that idea. It is a formal, slightly bookish word; in speech people more often say “there isn’t any” or “it doesn’t exist.”