The random walk theory states that prior stock prices are not good predictors of future prices. Instead, stock prices behave in an unpredictable manner. Thus, an investor should not rely upon the trend of prior stock prices to predict future stock prices.
Those disagreeing with the theory state that there is a pattern to stock prices. If this is the case, one can earn a return by carefully selecting the prices at which shares are purchased and later sold. Also, the theory assumes that markets are efficient, where changes in financial information are immediately reflected in the stock price. If this is not the case, then there may be some pattern to ongoing changes in the prices of stocks.