Here, Hayek points out why decentralized decision making is universally more efficient than centralized (i.e., free markets are more efficient than centrally planned ones). First, let me point out that the superior efficiency of free markets is not in question. They are more efficient, end of story. From a policymaker perspective, some are willing to sacrifice that efficiency in order to gain more equality. This is accomplished through central planning (government takes taxes and redistributes it to the poor, taking a hefty chunk of it in the process to pay the people who facilitate the endeavor). Thus, society always faces a tradeoff between efficiency and equality. If you want more equality, you have to shave some success off of the top and redistribute it to the poor. If you want more efficiency, you have to let capital flow to its highest return (the rich...who have a knack for taking capital and making more of it).
Back to the subject: Why is there more efficiency in free markets than in centrally planned ones? It is simple. Knowledge about the availability and desirability of any good or service is necessarily dispersed throughout the entire population (read: everyone has an idea about what stuff they want). A central authority could never (ever) hope to have this same level of knowledge. They would just be guessing (read: the government can guess what you want, or decide what you need, then try to give it to you). Thus, what type of economic system best utilizes the vast amount of knowledge present at any given time in a population? The answer: that system which leaves the decision making in the hands of the people with knowledge.
In Hayek's words: Which of these systems is likely to be more efficient depends mainly on
the question under which of them we can expect that fuller use will be
made of the existing knowledge. And this, in turn, depends on whether we
are more likely to succeed in putting at the disposal of a single
central authority all the knowledge which ought to be used but which is
initially dispersed among many different individuals, or in conveying to
the individuals such additional knowledge as they need in order to
enable them to fit their plans with those of others.