There is no exact definition of an expert system, but it's generally agreed that expert systems:
Technically speaking, most expert systems are and were (like production systems) relatively uninteresting, being logic-based programs which used simple inference methods to reason over their rules. However, they played a large rôle in making AI visible to business and government. This had an enormous, but not necessarily beneficial, effect on the funding of AI research.
Expert systems also made the study of human-computer interaction more important. A simple rule-based expert system can easily be programmed to generate automatic explanations of how it has reached a conclusion, or why it is asking a question. However, these explanations leave a lot to be desired, being too detailed and low-level. These defects stimulated work on systems which give a more structured overview of their reasoning, and even ones which tried to adapt to their user's level of skill.
The rules that make up an expert system's knowledge are often gleaned from human experts. This spawned a new subject of knowledge engineering or knowledge acquisition. Psychological skill was important to make sure that the experts told you what they knew, rather than what they thought they knew.
In general, expert systems are not intended as cognitive models. It helps (in some cases), if a system reasons in a way that a human can understand. However, we're not usually aiming to produce a detailed model of the expert, merely a tool which can solve the same problems. Because of this, and because of the technical simplicity of most expert systems, I shan't say much about them. In any case, if you understand production systems, you won't find rule-based expert systems difficult.
For a view from the heights of commercial interest, skim [Guide to Expert Systems]. This was written in 1985, near the top of the expert systems boom. Indeed, the book was a result of this. A new expert systems journal had just started up, intended for a business audience. The book was to be given away (or sold cheaply) to new subscribers with no knowledge of AI, as a way of easing them into the subject. The book contains numerous examples of expert systems and a brief description of inference, and exemplifies the optimistic attitude of its time.