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An explanatory model is a useful description of why and how a thing works or an explanation of why a phenomenon is the way it is. The explanatory model is used as a substitute for "the full explanation" of the thing in question:
- either because the full explanation is unavailable
- or because the full explanation is too cumbersome to be practical in the case at hand.
Explanatory models do not claim to be a complete description/explanation of the absolute about the thing/phenomenon, nor do they even claim to, necessarily, be fully accurate. The description/explanation does, however, need to fit well enough to a sufficient portion of all the knowledge, observations and theoretical circumstances known about the thing/phenomenon, so that the explanatory model becomes useful. That is: the description/explanation in an explanatory model, should be useful/helpful when one is about to make a decision or choice or when trying to successfully understand, explain or in some other way relate to the reality of the world around.
Use of the term
As most, if not all, explanations of anything, to a certain degree depend on axioms, and thereby are incomplete and not really "the full explanation", then, strictly speaking, all explanations are in fact explanatory models.
Yet, the term "explanatory model" generally is used only when one feels the need to emphasize awareness of the incompleteness of an explanation (due to intentional simplification or due to lack of knowledge and understanding).
By being mindful of the difference between on the one hand: "absolute reality" and on the other hand: "the explanatory models that one has become accustomed to", then one will be better equipped to avoid erroneously rejecting important new knowledge, even when this new knowledge seem to clearly contradict that which one "knows" from before.