We don't hold a narrow definition of exactly what a 'visual model' should look like: they should use whatever visual elements or styles – diagrams, maps, graphs, charts, pictures, cartoons, etc. – that will most effectively represent the problem at hand.
We can however define visual models by what they strive to do, and list a some of the important characteristics that distinguish 'visual models' from other kinds of graphic art.
Visual Models:
• render conceptual knowledge as opposed to quantitative data (information visualization) or physical things (technical illustration). We usually express conceptual knowledge with words alone, and yet the meaning behind those words is often inherently visual. Visual models seek to render directly the image-schematic meaning that lies behind our words.
• should be good models - the images should accurately reflect the situation in the world and embody the characteristics of a useful model.
• integrate the most salient aspects of the problem into a clear and coherent picture.
• fit the visual structure to the problem – and not force the problem into a predefined visual structure.
• use a consistent visual grammar.
• should be visually and cognitively tractable. Visual models exist to support robust qualitative thinking: they're software for 'human-simulation' (as opposed to computer-simulation) of the issue at hand. To serve as effective 'simulation software', visual models must be 'readable' and 'runable' by our visio-cognitive 'hardware' and should positively engage our prodigious visual intelligence.
• tap into the power of elegant design. In other words, they shouldn't be ugly.
Due to the limited capacity of our working memory, 7 ± 2 ‘chunks’ of information, we cannot hold in our minds concepts, arguments, or problems that consist of more than 5 to 9 objects or relationships. While this cognitive limitation severely restricts our ability to think about complex things, we can do what we often do: extend our intellectual abilities with external representations or 'models' of the problem.
The particular affordances diagrams – their ability to simultaneously show many objects and relationships – make them an ideal tool for thinking about conceptually-complex problems. Diagrams provide an external mnemonic aid that enables us to see complicated relationships and easily move between various mind-sized groupings of things.