Many organizations start out as privately-held companies. The organizers, or founders, get together and issue themselves stock in the company according to their contributions, which can be financial (money), intellectual or real property, or the amount of work they expect to do, or some other factor. That stock represents an ownership of the company, and they can issue additional shares to themselves, or to new hires perhaps in the form of options. They can also sell stock to other qualified individuals (usually considered to be experienced investors), but not to the general public. Holders of stock can be compensated in a number of ways. If the company is making a profit, some of that money can be returned to the shareholders as dividends which could be divided up according to the proportional ownership of shares. Companies don't have to pay dividends, though. Profits can be reinvested in the company to help it grow, increasing the value of the shares themselves. The increased value of the shares will be valuable if the shares are sold to someone else, or bought back by the company.
One of the nice things about privately held companies is that the individual shareholders are not personally liable for the debts of the company. What this means is that if you are an employee shareholder or an investor in a company that goes bankrupt, the creditors can't come after you to pay the bills. This limitation of liability is an important aspect of corporations and makes it possible to raise money from investors who can benefit if the price of the stock increases, but aren't liable for the debts if the company fails.
Another nice thing is that privately-held companies don't have to publish their financial status to the world. Since the general public can't buy and trade the stock it is assumed that the experienced investors will have the intelligence to ask the right questions and evaluate the investment opportunity.
