In a general sense, underwater describes a financial instrument that from the holder's perspective is worth less than the value of the collateral it is attached to.
Traditional mortgages require a buyer to have a downpayment before the lender will finance the deal. If a buyer were to put 20% down on their home and mortgage the remaining 80% to a lender, the 20% the buyer paid is known as equity. Should the appraised value of the home drop (as is the common experience in 2007 and 2008), equity diminishes. Should the home's value drop to 70% of the purchase price, if the borrowers still owe 80% of the home's original value, they are said to be underwater.
To sell the example home at this point, the owners would have to pay an additional 10% to the mortgage lender or make alternative arrangements, such as a short sale.