When investors talk about stocks, they usually mean "common stocks." A share of common stock represents a share of ownership in the company that issues it and ties the investor's fortunes to those of the company. The price of the stock goes up and sown, depending on how the company performs and how investors think the company will perform in the future. The stock may or may not pay dividends, which usually come from profits. If profits fall, dividend payments may be cut or eliminated.
Many companies also issue "preferred stocks". Like common stock, it is a share of ownership. The difference is that preferred stockholders get first dibs on company dividends in good times and on assets in bad times, if the company goes broke and has to liquidate. Theoretically, the price of preferred stock can rise or fall along with the common. In reality it doesn't move nearly as much because preferred investors are interested mainly in the dividends, which are fixed when the stock is issued. For this reason, preferred stock is really more comparable to a bond than to a share of common stock.
It's hard to think of a reason to buy preferred stocks. They generally pay a slightly lower yield than the same company's bonds and are no safer. Their potential equity kicker (the chance that the preferred stock will rise in price along with the common stock) has been largely illusory. Preferred stock is really better suited for corporate portfolios because a corporation doesn't have to pay federal income tax on most of the dividends it receives from another corporation.
There are lots of reasons to own stocks and several different categories of stocks to fit investors's goals. Sometimes the reasons for buying a particular kind of stock are obvious from the definition of the category.
Common stock and preferred stock are the two main forms of stock; however, it's also possible for companies to customize different classes of stock in any way they want. The most common reason for this is the company wanting the voting power to remain with a certain group; hence, different classes of shares are given different voting rights. For example, one class of shares would be held by a select group who are given ten votes per share while a second class would be issued to the majority of investors who are given one vote per share.