A mortgage is said to be "underwater" when the amount owed is greater than the value of the property. When a mortgage is underwater, the owner can't sell the property for what is owed on it. This makes it nearly impossible for the owner to move to a different area since no one is going to buy the home at an above market rate.
In some cases, debtors can work with the bank to arrange a short sell where the property is sold for less than it is worth and the bank takes a loss. In other cases, the owner will stop making payments and default on the loan. At this point the bank will normally foreclose and take back the property in order to try to sell it.
There are people who are underwater on their mortgage who are still capable of making the payments. A good number will simply wait for the housing market to return, but some are making strategic defaults where they stop making payments in order to make the bank take back the collateral (the house).