Stock options are provided to employees, executives, etc. of companies for various reasons: bonuses, additional compensation when the company is struggling and can't actually pay you in cash, etc. Essentially, the way they work is that when they are "given" to you, you have the option to "exercise" them, which means that you buy them at the price that the stock is currently at.
The main difference between stock options and regular stock is that the price of the options is kept at the price it was when the options were issued, called the "strike price." When and if the stock exceeds the strike price by a suitable margin, the individual exercises the options and generally sells the stock at the same time, earning the difference in profit. (I've forgotten if the individual can keep the shares if (s)he so desires.) So for example, if you had 1000 shares in options of a company, each with a strike price of $5, and a company's share value rose to $7, you could exercise those options and net $2000.
The other main difference is that there is a timeframe set for exercising stock options when they are issued; after this point they "reach maturity" which actually means they cease to exist. So if you don't exercise them within that timeframe, you lose them, end of story.