On the surface, it might seem a little crazy for a bank to release a lien on a property for less than the total amount owed.  However, when you look at the whole picture, a short sale really makes a lot of sense for the lender as well as for the borrower.
When a house is worth less than what is owed and the homeowner can no longer afford his payments, the bank only has a few options.  Here are the most common:  work out some sort of modification on the loan (lower the interest rate, waive late fees, add back payments to the end of the loan, etc.) that brings the borrower current and makes his payment affordable; foreclose on the home; or work out a short sale.
Because the lack of income that originally got the homeowner into trouble, modifications are a realistic option for relatively few borrowers.  Foreclosure is an incredibly expensive process for the bank.  And when the foreclosure is over, the house is usually worth less money than it was before the foreclosure process began.  By working a short sale, the bank is able to avoid the expense of a foreclosure, eliminate carrying costs that come with owning the home, and sell the home for more money than it is likely to bring after the foreclosure. 
The bottom line is that short sales cost the bank less in time, money, and resources.  And banks are all about the bottom line.  If you would like to learn more about short sales, check out our website at HomeSaverGuys.com.