The beta of the stock of a company is the correlation of the value of the stock and that of the benchmark indices of the market. A market's benchmark index like the NASDAQ, DJIA, etc. is computed using the average stock value of a small number of selected companies that statistically represent how all the companies in the market are behaving.
For example, if a technology company has a beta value of 1 with respect to the NASDAQ, an increase of x% in the NASDAQ is accompanied by an increase in the price of the stock by x%. On the other hand companies with high beta values display a change in price that is many times that of the change in the benchmark index. This makes them good to hold on to if the market is going up. But high beta companies also fall drastically if there is small decrease in the value of the benchmark index. A company with a beta value of 2 compared to the DJIA would rise by 2% if the value of DJIA rises by 1% but if the DJIA were to fall by a percent the value of the company's stock drops by 2%.
High beta companies can give expected returns many times higher than low beta companies when the markets are rising but when the markets fall the same companies could lead to large losses. High beta companies are high-risk, high-return investment options while low beta companies give lower returns but at the same time also have a lower risk.