Answer: the formal theoretical determination governing the process of thought. Thus, main definitions, as those concerning all formal aspects, such as ‘form, matter, time, space, structure, etc.’ should be determined in a metaphysical frame, which should also include, if possible, the process through which knowledge is obtained (theory of understanding or knowldege) in order to allow the validation through marks of truth or even reality deriving from the former. In usually contained also the logical process of validation (Aristotle, Kant).
It is called mataphysics because it refers to question laying ‘beyond physics’ without though being determined as such as ‘ideal’, as concerning the ‘form’ or ‘way’ determining knowledge. Physics should be understood not as ‘science’ (physics) but as ‘material’ (physis: the nature as nature or as nature of something, also called substance).
In general it concerns all abstract term that may not be grasped through eyes, fingers, ears or taste and smell. Conclusion: to be a metaphysician is a hard job. To define a metaphysical background, almost impossible. But, if you differentiate two main metaphysical currents, you may discern ’empricism’ and ‘idealism’ as ruling most metaphysical theories. It is enough to put a general theory into one or the other in order to pretend to a metaphysical background.