A home loan goes "underwater" when the homeowner is left owing more than the property is worth. Underwater mortgages usually don't happen when the homeowner is on their first home loan; they generally come about when a second or third mortgage is signed, or when economic conditions cause property values to drop.
One of the easiest ways to get underwater on a home loan is when a mortgage is refinanced. The typical lender might offer the option of borrowing against the equity built up in the home; if there is a lot of equity in the home this is actually a viable option. However, if the amount of equity is small, the homeowner can easily end up owing more than their home is worth.
Underwater home loans can also happen when property values shift greatly. When changes such as rezoning take place, a property's market value can easily drop below the value of the mortgage, creating a situation where the owner could not sell for enough to pay their mortgage.
In other cases, underwater mortgages happen when the borrower takes out too many mortgages. There are lenders that offer third mortgages based on job and credit history, but if the homeowner becomes unemployed and can't keep up with payments, that third mortgage puts them underwater.
Shifts in the housing market can also create underwater home loans. When the demand for homes exceeds the local supply, home prices will rise, resulting in a corresponding rise in the home and mortgage markets.
When the bubble bursts and the markets decline, homeowners end up owing more than their property's market value. At that time, they can't sell the home for a sufficient amount to pay the mortgage, and they are much more likely to go into default.