LNG Chart, page-24

You can sell shares you don't own by borrowing them from someone else (for a fee). You sell the shares in the hope that you can buy them back at a cheaper price in the future. Once you've bought them back you can return them to their owners. If you manage to buy them back at a cheaper price you have profited the difference between the price you sold them at and the price you bought them at. However if you can't buy them back cheaper and end up buying them back at a higher price you have lost the difference between the price you paid and the price you sold at. Usually there is a limit on the period of time you can borrow the shares for (hence short sell).