An initial public offering, or IPO, is the first sale of stock by a company to the public. A company can raise money by issuing either debt or equity. If the company has never issued equity to the public, it's known as an IPO.
Companies fall into two broad categories: private and public. A privately held company has fewer shareholders and its owners don't have to disclose much information about the company. Anybody can go out and incorporate a company: just put in some money, file the right legal documents and follow the reporting rules of your jurisdiction. Most small businesses are privately held. But large companies can be private too. Did you know that IKEA, Domino's Pizza and Hallmark Cards are all privately held?
It usually isn't possible to buy shares in a private company. You can approach the owners about investing, but they're not obligated to sell you anything. Public companies, on the other hand, have sold at least a portion of themselves to the public and trade on a stock exchange. This is why doing an IPO is also referred to as "going public."
Public companies have thousands of shareholders and are subject to strict rules and regulations. They must have a board of directors and they must report financial information every quarter. In the United States, public companies report to the Securities and Exchange Commission (SEC). In other countries, public companies are overseen by governing bodies similar to the SEC. From an investor's standpoint, the most exciting thing about a public company is that the stock is traded in the open market, like any other commodity.