The simplest definition of market efficiency is that the price already reflects the available information and thus buying or selling the stock should, on average, return you only a "fair" measure of return (after transaction costs) for the associated risk.

Summary: The basic point is that beating the market is incredibly difficult and market efficiency should not be confused with market perfection.  Markets are not perfect, but they are very tough to beat.
 

Here are my class notes on the Efficient Market Hypothesis (EMH).   SOme notes form my newsletter on market efficiency.

I also highly endorse (require for my classes) reading Ray Ball's Theory of Stock Market Efficiency: accomplishments and limitations.  It is published as part of Chew's The New Corporate Finance.  Additionally Fama, 1991,  has an excellent summary article on market efficiency.   Both of these are summarized on my summaries page.

Possibly less academic in nature but more convincing in reality is the fact that so few people or mutual funds either in the US, or abroad,  actually beat the market on a risk adjusted basis.
 

Some other links that should help you with market efficiency
Investopedia.com has some notes
Martin Swell has complied some notes on efficeint markets that are quite good!  (there I tried to be British) ;-)
Dean Lebaron has a very good look at the EMH--largely from his book which I HIGHLY recommend!

Although many in finance now believe that markets are efficient, it is not unanimous.   One group of these people are technical analysts.  These people believe they can predict price movements based on historical prices (a clear violation of weak form efficiency).   Although the vast majority of academic papers finds no benefit to technical analysis, it has long been difficult to explain why there are technical analysts around (how can we say the market is inefficient in keeping technical analysts while say it is efficient in other things).  Several recent academic papers have at least suggested that technical analysis might not be worthless.  While others have followed with some excellent research, the main person here to remember is Lo.  He has had two very good articles on technical analysis.  To see the background try this from the Review of Financial Studies.   He also has a JF paper with Mamaysky, Wang (JF)--abstract   that concludes that technical analysis may not be as bad as we previously thought.

Here are some interesting links on technical analysis
The Equity Research Center has a nice page decribing the differences between technical and fundamental analysis
Marketscreen.com has a good review of what techincal analysis is and even provides some examples
Dean LeBaron should teach: He is interesting, looks at both sides, and usually gets it right! Here is his take on technical analysis.

Another big challenge to market efficiency (and the implied assumption of investor rationality) is behavorial finance.  It is one of teh hottest fields in finace now and there is mounting evidence suggests that investors sometime act irrationally.  This may or may not be a problem.  Remember that certain investors can act irrationally so long as the marginal investor (the one who sets the price) does not.  However, as the evidence grows, many (including myself) are acknowledging that behavioral finance does play a role in how finance works.  (That said, many of the behavioral finance stories can be refuted or at least questioned.--see Fama 98?) .
 

Links on Behavirial finance
Behavourialfinace.net
Stanford provides a nice intro and even some examples
A working paper by Barberis-Thaler
The top ten behavorial finance downloads from FEN (updated monthly)