They describe quite a number of cognitive tests that demonstrate how little we actually know, and how strongly we over-evaluate our own knowledge. They explain the 'Illusion of Explanatory Depth' (which demonstrates how shallow our knowledge is of evern everyday things such as zippers and flushing toilets), they explain how our perceptions fool us by (re)constructing the gaps in our vision for instance. They explain the Illusion of Comprehension when you think you understand it because it looks familiar (as in a student re-reading his course without integrating the knowledge).
Their theory is that the mind is actually much broader than the individual. You don't store information because you know it's available elsewhere (as with the natural distribution of sharing knowledge within couples: tasks of storing information becomes divided). There is the obvious 'groupthink' that reflects the unquestioned beliefs and assumptions that you take over from the group you belong to.
Our brain has evolved to work properly in an action-oriented environment. Sufficient to act in different circumstances, driven by a simple cause-and-effect logic.
It's a humbling book because of all the flaws that we have in our thinking, the faulty perceptions, the lack of logic, the overestimation of our own capacities, the shallow memory, etc. At the same time, it is also enriching, in the sense that it demonstrates that in specific circumstances, we can obtain strong results by collective thinking, by adding different perspectives to our own. We are social animals, and by listening and challenging and enriching each other, we can challenge assumptions, misperceptions, and other illusions.