An efficient market is one in which securities prices reflect all available information. This means that every security traded in the market is correctly valued given the available information.
There are a number of different definitions of what constitutes an efficient market depending on the what information is deemed to be available.
Weak form efficient markets
The weakest form of efficient markets is that securities prices reflect all information contained in historical prices. This is the easiest to prove, by showing that share prices follow a random walk.
It is this form of efficient markets that technical analysis rejects, and neither the track record of technical analysis as a strategy or the evidence from studies of historical prices, provide reasons to reject it.
Some investors have successfully used statistical arbitrage techniques. However only a minority of the actual trades make large profits, so the deviations from market efficient are, on average, small and they are expensive to find.
Semi-strong form efficient markets
The semi-strong form of efficient markets is that securities prices incorporate all publicly available information. Given how difficult it is to find groups of “smart” investors who consistently outperform the market, this seems likely. There do seem to be some investors with very impressive records. The semi-strong efficient markets hypothesis is probably very close to being true, but not always true.
There is evidence that smart investors do out-perform. This probably reflects access to better information rather than better analysis of information that is available to all.
Strong form efficient markets
The strongest form of efficient markets is that prices incorporate all information that any investor can acquire. This seems unlikely given that insider traders can undoubtedly make money fairly consistently.
Not only do insider traders make money, but in most situations where insider trading takes place prior to the public release of price sensitive information the price move significantly on the public release of the information. Therefore the non-public information was not fully reflected in the price.
No free lunch vs. correct pricing
Some comment on the efficient markets hypothesis describes two different interpretations of it: that prices are “correct”. While conceptually interesting, this is somewhat unscientific because it is difficult to construct empirical tests that distinguish between the two: most attempts to test efficient markets try to prove that strategies exist that will consistently out-perform the market (using only the data appropriate to the form being tested).
Known market inefficiencies
The most glaring exceptions to efficient markets seem to occur during investment bubbles and collapses when prices reach levels that can not be explained by reasonable valuation methods. As a result, there are often great inconsistencies in how different investments are valued and these violations of the law of one price are, in themselves, evidence that markets are inefficient.
However, the bulk of the evidence is that in favour of the efficient markets hypothesis stands up pretty well. See Eugene F. Fama’s (somewhat old) classic review of the evidence. The best approach is to treat it (like capital structure irrelevance), as a normative model, deviations from which provide insight into how markets work — except that the efficient markets hypothesis is also a very good model for how markets work most of the time.