A stock option is a contract to buy (known as a "call" contract) or sell (known as a "put" contract) securities, often shares of stock, at a predetermined or calculable (from a formula in the contract) price.
For example I may own an option to buy a share in XYZ corp. for $100 in one months' time. If the actual stock price at the time is $105 then I would "exercise" (i.e. use) my option and buy a stock from whoever sold me the option for $100. I could then either keep the stock, or sell it in the open market for $105, realising a profit of $5. However if in one month's time the stock price was only $95, I would not exercise my option, as if I really wanted a share in XYZ Corp, I could buy it in the open market for $95 rather than using my option to buy it for $100. Thus if I have an option, I might make a profit and am certain not to make a loss. This means an option must have some positive monetary value itself. The problem of calculating exactly the how much that option is worth has been the subject of much academic and practical interest for the last 40 years. The most popular method used in the financial markets is to use the Black-Scholes formula, but this depends on the option style.
Options themselves are traded as securities on stock exchanges. Stock options for the company's own stock are often offered to upper-level employees as part of the executive compensation package, especially by American business corporations. Because stock prices are related to corporate earning, the granting of stock options gives an employee an incentive to increase earnings, either in reality or possibly by the use of creative accounting. It is estimated that over-reporting of income by an average of 25% by American corporations was one cause of the Stock Market Downturn of 2002.