Defining Mental Models
A mental model (aka mental representation/image/picture) is a mental structure that attempts to model (depict, imagine) how real or imaginary things look like, work or fit together. Thus, a mental model can correspond to an object, idea, a collection of information, objects or ideas, or anything else, concrete or abstract, that the mind is thinking about  consciously or unconsciously. The mental structure behaves likes an ‘analogical representative’ of the thing envisioned  being an abstraction as certain characteristics are eventually left out, either because are irrelevant, poorly understood, not perceived or simply forgotten.
A mental model is a blend of mental content — beliefs, assumptions, concepts, meanings, thoughts, intuitions, ideas, icons, symbols, analogs, metaphors, memories and even psychological or spatial-temporal contexts, together with the relationships existing between them. I tend to believe that a mental model doesn’t necessarily have a definite structure within our mental space given the dynamics nature of its components. We are talking here about multiple substrata of meaning that can move beneath as the currents of a sea without the sailor being aware of it. The beneath currents are nothing but pulls, pushes and swings of the mental processing taking place inside the mind.
Even if they appear to have unity, mental models are rather amorphous or multifold. The unity is apparent, derived from their iconic aspect — when we look from above, they seem to have unity, however when we look under microscope at them the unity dissipates into the multitude of relations. To delimit a mental model’s structure one can make a cut when the relationships become weaker and weaker however also this weakness is apparent. Moreover, the mental space seems to be a combination, recombination, aggregation and overlapping of mental models that resemble the structure of a hypergraph.
A mental model is also a mechanism of explaining how the mind works, how it can perceive and represent reality, think, imagine, etc. Therefore, the mental models we hold are mainly unconscious unless we make them conscious when we start to evaluate their structure, delimitate their boundaries in one form or another, respectively identify the effect they have on us.
When one attempts to externalize a mental model into a form of representation then it becomes an external model, however it might need several adjustments spread over several iterations before it can become self-contained. During this process our internal model might change as well as new understanding is gained, as gaps in understanding are filled with facts, assumptions or other mental content.
In reverse, one attempts understanding a model, the internal projection being one or more mental models depending on our understanding and its various interpretations we depict. This might happen unconsciously as we acquire knowledge or the mind does its inner workings, or consciously when an active component is involved — playing with the model, analyzing its advantages, disadvantages, areas of applicability, presumptions, etc.
Some suppose that there’s a one-to-one mapping between an external and a mental model, thing which is not necessarily true. A many-to-many relation is more plausible considering that there can be multiple interpretations of an external model, and a mental model can result in multiple external models with different abstraction levels.
Several resources consider the mental models only as representations of external things though they can be also representations of fictitious things or even processes that take place within the mind. In the end, mental models are mental analogs of physical models as they attempt to abstract some of the important features of the reality or some aspects of it. Moreover, many of the characteristics of external models apply to mental models as well.