Beta is usually used with reference to the stock of companies and is the change in the stock price with respect to the change in the value of a benchmark, which is usually the stock market index.
The stock market index gives a weighted average of the change in price of the stocks of all the companies that are traded on the exchange. A change in the index due to a change in the price of the stock of small companies is negligible. This is the reason why the stock market index is made up of a select number of companies which have the largest market capitalization.
For the stock of any company, the average change in its price compared to the change in the value of the stock market index is known as Beta.
A Beta of more than one implies that the price of the company's stock price changes by a value that is more than the change in the stock index price. For example, a stock with a Beta of 1.8 would increase by 18% if the value that the index increases by is 10%. Beta can also be less than one and in some cases can even be negative.
Risk increases with an increase in Beta. This is due to the fact that the value of the stock market index can move up as well as down. Just as a high beta stock's price would rise up by a value higher than an upward change in the stock market index, when the index drops the high beta stock price shows a much larger drop in price.
The Beta of a stock is taken as one of the important measures of risk and, when stock is bought or a portfolio is created, the Beta is kept at a level that suits the risk appetite of the investor.