A short sale is when the property is sold for less than what is owed. This is done to avoid foreclosure.
A short sale is started when the home-buyer (borrower) has a hardship and can no longer afford the home. The bank (or lender) has to first agree to the putting the home on the market as a "short-sale" and then accept an offer for less than what is owed.
Short sales are a benefit to the borrower and lender in that it avoids timely and costly foreclosure procedures, the home is usually left in better condition than if it was vacated or abandoned, and because the bank agrees to the short-sale offer, does not go after the borrower for the remaining balance (or deficiency).
If you are the person buying the home in a short-sale situation, you are probably getting a good deal, and your credit is not damaged by the transaction at all (given you pay as promised).