His major early contribution was to show that stock markets are efficient (See efficient capital markets). The term "efficient" here does not mean what it normally means in economics--namely, that benefits minus costs are maximized. Instead, it means that prices of stocks rapidly incorporate information that is publicly available. That happens because markets are so competitive: prices now move on earnings news within milliseconds. If someone were certain that a given asset's price would rise in the future, he would buy the asset now. When a number of people try to buy the stock now, the price rises now. The result is that asset prices immediately reflect current expectations of future value.
One implication of market efficiency is that trading rules, such as "buy when the price fell yesterday," do not work. As financial economist John H. Cochrane has written, many empirical studies have shown that "trading rules, technical systems, market newsletters and so on have essentially no power beyond that of luck to forecast stock prices." Indeed, Fama's insight led to the development of index funds by investment management firms. Index funds do away with experts picking stocks in favor of a passive basket of the largest public companies' stocks.
Fama's insight also has implications for "bubbles"--that is, asset prices that are higher than justified by market fundamentals. As Fama said in a 2010 interview, "It's easy to say prices went down, it must have been a bubble, after the fact. I think most bubbles are twenty-twenty hindsight. . . . People are always saying that prices are too high. When they turn out to be right, we anoint them. When they turn out to be wrong we ignore them."
This is from "Eugene Fama," which has recently been added to The Concise Encyclopedia of Economics. It is a propos, given the recent discussion of stock prices on Econlog (here and here.)