In Short: Outstanding shares are all the stock that is owned by all the shareholders. So, you invest in company ABC. ABC has 10 million outstanding shares; this means that all the profits, earnings, are shared among those 10 million shares.
This means that as a company has more and more outstanding shares, each share has a much smaller piece of the total profits of the company. The number of outstanding shares in a company also is not static. This number can change over time and it is important to keep track of so you, as a shareholder, know what your shares are actually worth.