Simply, it's when the sale of the house is less than what the owner still owes on the mortgage. Many lenders will agree to a short sale and forgive what is owed on the mortgage when the owner cannot make the payments due to financial hardship. As a result, the lender can avoid a sometimes lengthy and costly foreclosure, and the owner can pay off the loan (although their credit could be harmed due to a short sale).
That is the simple answer. A more realistic look is covered in this thread "What is a short sale?" in Zillow Advice. In particular, there is a comment by Tallahassee real estate broker Fred Griffin that offers an answer filled for sage advice for the seller and the buyer.
For anyone contemplating a short sale -- whether you're a seller or buyer -- make sure you get the advice of an attorney that specializes in short sales to avoid tax and legal implications down the road.