When we understand something—let’s say a concept, like a table—we have some formulation of that “in our head”. That formulation is something we can manipulate while we’re thinking or conversing or acting.
If I ask you to think of a green table with straight silver legs, you manipulate a model in your head to try to understand what I mean. The name for this formulation in your head is a model or, more accurately phrased, a conceptual model. (More about models in general here.)
When we know how to use something, it’s because we have a conceptual model of that thing. Now, if we’re designing something, we can design better if we think about the conceptual model of a person using it—the model they have before they start using it, the model they need to use it well.
But here’s a great presentation about the role of conceptual models in IxD that goes into all that beautifully—lots of examples and even Steve Job’s definition of design.