Shares outstanding is the numbers of shares of common stock the company actually issues including stock that is held by the public, officers, and insiders, but excluding repurchased shares. This number includes all the shares that can be bought and sold by the public, as well as all the restricted shares that require special permission before being traded.
Not all the shares that a company can be divided into are available for trading, or even can be traded. There's the authorized shares, there's the issued shares, and then there's the outstanding shares. The first is how many shares there could be traded. The second is how many have ever been traded (including those bought back as treasury shares). The last is how many can actually be traded, if all conditions were met.
It is the shares outstanding that is used to determine earnings per share (EPS). It is also used to determine the market capitalization of the company (multiply the share price by the total shares outstanding).
To find this number look at the most recent 10-Q or 10-K issued by the company. The number should be within the introductory stuff, up near the address and official name. It can also be found in the shareholders' equity portion of the ]]balance sheet]]. The number will fluctuate over time as the company sells more shares, buys back shares, and retires shares. It could be a red flag, meaning look further and sell if necessary, if the company's outstanding share count rises faster than about 3% to 5% per year. If it rises faster than that, especially if it is rising faster than revenue or earnings is growing, current shareholders are getting diluted by the new shares and are owning smaller and smaller pieces of the company.