Models—good ones, anyway—are valuable in a number of ways.
The best resource I know on the topic is the paper Models of Models by Hugh Dubberly.
You might want to start there. Here’s what Dubberly writes:
Models are ideas about the world—how it might be organized and how it might work. Models describe relationships: parts that make up wholes; structures that bind them; and how parts behave in relation to one another.
For example, the sun rises in the east, moves across the sky, and sets in the west. Or the earth orbits the sun. Models support communication and learning. Models help bridge the gap between observing and making, between research communities and design communities. Models are especially important in interaction and service design.
See especially the last two sections of his paper, about how to judge mental models and how to judge visual representations. And those sections make an important distinction: it’s useful to reserve the meaning of “models” to be the definition from Dubberly quoted above—”ideas about the world”. Ideas are “in our heads.” If we make a diagram of our model on paper or screen, there can be many advantages: we understand our own (mental) model better, and we can use the visual representation or diagram to communicate and collaborate with others, since it’s now “outside our head”.