Definitions
Models are “a complex set of interrelated hypotheses.”
Natural Experiments of History, P21, Jared Diamond
All models are wrong, but some are useful.
George Box, 1978.
Discussion
Regarding models being wrong, what is meant is that every model is an abstraction or representation of reality, and in so being, a model is incomplete, probably inaccurate, and it may even not even be fit for its intended purpose. But, if a model helps more than it hinders, then perhaps it is then useful.
Leaving aside the possible differences between reality and what we perceive (construct in our minds) reality to be, the only true representation of reality is reality itself. Anything else that purports to represent reality, such as a model, where an example would be the stylised schematic of The London Underground rail network, is by necessity a simplification – there is simply far too much information out there in reality for us to comprehend and make sense of anything more than a small subset of it let alone the whole thing.
Paraphrasing Shane Parrish[1] of Farnham Street, mental models describe how the world works. Being a simplification of reality, at whatever level of simplification we need for the context or our level of interest or expertise, models help shape how we understand, think, and form beliefs. Models are often subconscious, such as our expectations of the effect of gravity when we drop a rock on our foot, but they can also be conscious such as The 9-Forces Model. In either case, models help us to focus on what is relevant and to discount what is irrelevant to our context. We use models to infer causality, recognise and match patterns, and draw analogies; models are the means by which we think and reason.
[1] The Great Mental Models, Shane Parrish.