It frequently happens that a business finds itself in need of a lot of money, very quickly. When it does, the most common way to raise capital is through a stock offering. With the help of an investment bank, a business can package itself into a number of individual shares of stock - anywhere from a few thousand to many millions - and then allow these shares to be offered for sale to investors. Most stock offerings are public, though companies do also have the option of making private placements.
Stock represents private ownership of a company. The more shares owned by an individual investor, the greater that investor's stake in the company. For example, if company XYZ offers shares of itself to the public for the first time in the number of 100,000,000 and you buy one, then you own exactly one hundred millionth of that company. And if the Goldman Sachs Group purchases 6,500,000 shares of the same company, then the Goldman Sachs Group owns 6.5% of it.
Owners of a company participate in that company's financial success, and failure. After subtracting whatever debt it owes, the assets owned by a company are the legal property of its shareholders. In addition, every share of stock entitles its owner to a dividend payment (if the company offers dividends) and, more significantly, a vote on important company matters. One of the most important company matters that's taken to the polls is the choice of who will sit on the board of directors. The BOD oversees the company's operations. By voting for members of the board, investors have some say in the business' management and overarching strategy without directly participating in day-to-day operations. BOD candidates are usually nominated from within the company - either by executive management, the current BOD or, rarely, employee unions - but it is not uncommon for very large shareholders to manuever a nomination. This is usually accomplished after much barganing, and perhaps some threats of divestment. Corporate take-overs are often begun this way.
There are two kinds of stock, common and preferred.