Learning how to behave is more the source than the result of insight, reason, and understanding. Man is not born wise, rational and good, but has to be taught to become so. It is not our intellect that created our morals; rather, human interactions governed by our morals make possible the growth of reason and those capabilities associated with it. Man became intelligent because there was tradition--that which lies between instinct and reason--for him to learn. This tradition, in turn, originated not from a capacity rationally to interpret observed facts but from habits of responding. It told man primarily what he ought or ought not to do under certain conditions rather than what he must expect to happen.(Note: the emphasis is all Hayek's.)
This view is the result of Hayek's own studies and reflections on history and anthropology, and it provides a foundation for his anti-rationalist epistemology. I find myself lately rather hooked on this principle, as I see that it has far-reaching consequences. In education, for instance, I think we often see two schools of thought: one assumes that children are naturally gifted with the ability to think for themselves, and the other assumes that all knowledge must be handed down in the form of tradition. Hayek's principle is a little more favorable to the latter view, but even this will not suit: it is not merely knowledge which gets passed down through tradition, but a habit of thought enabling the mind to process things in an orderly fashion, for instance by the rules of deductive or inductive reasoning.
In terms of moral philosophy, I think this principle also leads us away from being (too) consequentialist in our reasoning. While it is often the case that our morals can be justified based on the general sort of consequence which we wish to avoid, there is in fact no way we can ever predict all the particular consequences of the various choices we make and the innumerable ways we make them. At bottom, we just have to accept that there are certain things you can't do, because, well, you just can't--even if you have some reason to suspect that it would be better in the long run if you did.
What goes mostly unstated in Hayek's moral philosophy is the underlying humanism implicit in his argument. Our morals have evolved to allow human beings to flourish to the greatest possible extent, given a world with ever-changing and unpredictable circumstances. This, for Hayek, is enough to place the benefit of the doubt on the morals we have inherited from tradition. On the other hand, it also justifies for him a great deal of skepticism about moral knowledge: "reluctant as we may be to accept this, no universally valid system of ethics can ever be known to us." One might call this the Incompleteness Principle of ethics, mirroring the Incompleteness Theorems of mathematical logic.
As a result, it is always possible to correct previous moral assumptions, either by showing some of our morals to be mutually incompatible or by showing empirically that some of our morals tend to do more harm than good. Such corrections can be continued ad infinitum, since no step in the process can ever produce the complete system of ethics we might strive for. What we absolutely cannot do is throw out traditional morality altogether and replace it with a plan by which we seek to deliberately conquer all obstacles to human flourishing. The dream of accomplishing this is exactly what Hayek names the fatal conceit. Not only will it not work, but it will backfire in devastating ways.
Hayek's moral philosophy is the right place to start if you want to understand the principles of a liberal social order of the "Hayekian" tradition, which, he would argue, goes at least back to the Scottish philosophers of the Enlightenment. But I think it's significant that, for a man known mostly for his thoughts on economics and politics, he had pretty brilliant insight into the complex and subtle relationship between reason, instinct, morals, and tradition.