The intuition behind the efficient markets hypothesis is pretty straightforward- if the market price of a stock or bond was lower than what available information would suggest it should be, investors could (and would) profit (generally via arbitrage strategies) by buying the asset. This increase in demand, however, would push up the price of the asset until it was no longer "underpriced." Conversely, if the market price of a stock or bond was higher than what available information would suggest it should be, investors could (and would) profit by selling the asset (either selling the asset outright or short selling an asset that they don't own). In this case, the increase in the supply of the asset would push down the price of the asset until it was no longer "overpriced." In either case, the profit motive of investors in these markets would lead to "correct" pricing of assets and no consistent opportunities for excess profit left on the table.
Technically speaking, the efficient markets hypothesis comes in three forms. The first form, known as the weak form (or weak-form efficiency), postulates that future stock prices cannot be predicted from historical information about prices and returns. In other words, the weak form of the efficient markets hypothesis suggests that asset prices follow a random walk and that any information that could be used to predict future prices is independent of past prices.
The second form, known as the semi-strong form (or semi-strong efficiency), suggests that stock prices react almost immediately to any new public information about an asset. In addition, the semi-strong form of the efficient markets hypothesis claims that markets don't overreact or underreact to new information.
The third form, known as the strong form (or strong-form efficiency), states that asset prices adjust almost instantaneously not only to new public information but also to new private information.
Put more simply, the weak form of the efficient markets hypothesis implies that an investor can't consistently beat the market with a model that only uses historical prices and returns as inputs, the semi-strong form of the efficient markets hypothesis implies that an investor can't consistently beat the market with a model that incorporates all publicly available information, and the strong form of the efficient markets hypothesis implies that an investor can't consistently beat the market even if his model incorporates private information about an asset.
One thing to keep in mind regarding the efficient markets hypothesis is that it doesn't imply that no one ever profits from adjustments in asset prices. By the logic stated above, profits go to those investors whose actions move the assets to their "correct" prices. Under the assumption that different investors get to the market first in each of these cases, however, no single investor is consistently able to profit from these price adjustments. (Those investors who were able to always get in on the action first would be doing so not because asset prices were predictable but because they had an informational or executional advantage, which is not really inconsistent with the concept of market efficiency.)
The empirical evidence for the efficient markets hypothesis is somewhat mixed, though the strong-form hypothesis has pretty consistently been refuted. In particular, behavioral finance researchers aim to document ways in which financial markets are inefficient and situations in which asset prices are at least partially predictable. In addition, behavioral finance researchers challenge the efficient markets hypothesis on theoretical grounds by documenting both cognitive biases that drive investors' behavior away from rationality and limits to arbitrage that prevent others from taking advantage of the cognitive biases (and, by doing so, keeping markets efficient).