Any business that wants to sell shares of stock to private or public investors needs to become a corporation first. The legal process of turning a business into a corporation is called incorporation.
If you start your pizzeria with your own money (even if it's borrowed from the bank), then you've formed a sole proprietorship. You own the entire restaurant yourself, you get to make all of the decisions, and you keep all of the profits. If three people pool their money together and start a restaurant as a team, then they've formed a partnership. The three people own the restaurant themselves, sharing the profit and decision-making.
A corporation is different, and it's a pretty interesting concept. A corporation is a "virtual person." That is, a corporation is registered with the government, has its own Social Security number (called a federal tax ID number), can own property, sue and make contracts. (It can also be sued.) By definition, a corporation has stock that can be bought and sold; all of the owners of the corporation hold shares of stock in the corporation to represent their ownership. One characteristic of this "virtual person" is that it has an indefinite and potentially infinite life span.
There is a whole body of law that controls corporations. These laws are in place to dictate how a corporation operates, how it's organized, and how shareholders and the public get protection. For example, every corporation must have a board of directors. The shareholders in the company meet every year to vote on the people who will "sit" on the board. The board of directors makes the decisions for the company. It hires the officers (the president and other major officers of the company), makes the company's decisions and sets the company's policies. Consider the board of directors as the virtual person's brain: Even if a corporation has a single employee who also owns all of the stock in the corporation, it still has to have a board of directors.
Another reason that corporations exist is to limit the liability of the owners to some extent. If the corporation gets sued, it's the corporation that pays the settlement. The corporation may go out of business, but that's the worst that can happen. If you're a sole proprietor who owns a restaurant, and the restaurant gets sued, you're the one being sued. "You" and "the restaurant" are the same thing. If you lose the suit, then you can lose everything you own in the process.
Let's talk more about the relationship between shareholders and corporations in the next section.