The random walk theory is the occurrence of an event determined by a series of random movements - in other words, events that cannot be predicted. For example, one might consider a drunken person's path of walking to be a random walk because the person is impaired and his walk would not follow any predictable path.
Applying the random walk theory to finance and stocks suggests that stock prices change randomly, making them impossible to predict. The random walk theory corresponds to the belief that markets are efficient, and that it is not possible to beat or predict the market because stock prices reflect all available information and the occurrence of new information is seemingly random as well.
The random walk theory is in direct opposition to technical analysis, which contends that a stock's future price can be forecasted based on historical information through observing chart patterns and technical indicators.
Academics cannot conclusively prove or agree on whether the stock market truly operates via a random walk or based on predictable trends because there are published studies that support both sides of the issue.