A short sale is a sale of your home where the amount you sell it for is less "falls short" of the balance you owe on your mortgage.  Short sales usually happen when the homeowner can't pay the mortgage on their loan and the lender decides it is better to sell the property at a moderate loss is better than pushing the borrower or letting the house go into foreclosure.  When you do a short sale as the borrower you are still responsible for paying the remaining balance (the difference between the sale price and the amount you still owed unde the mortgage) unless you vcan make some special arrangements with the bank.
 
The benefit of a short sale for the borrower is that they can get out of a house that is currently "under water" meaning the mortgage is more than the house is worth.  Many homeowners are in this situation today since property values have dropped dramatically over the past few years. 
 
If you don't think your house value will ever come back to the amount that you paid for it, or you are behind in your mortgage with no hopes of catching up, a short sale may be a good option for you.