Negative equity occurs when the value of an asset is less than the amount of a debt secured on it. It is most commonly used of mortgages on property, especially residential property, but may be applied to other types of security. It is a common cause of technical insolvency.
Negative equity is most often created when prices fall on a security that was originally adequate, but lenders also sometimes lend more than the value of the security (relying on the borrower's income and other resources) or because the terms of the lending allow payments of less than the interest due.
Negative equity is of most concern to borrowers when the loan has been made on a non-recourse basis. This means that borrowers can walk away leaving the lender with the entire loss. Of course, an insolvent borrower would also leave the lender with a loss, but it would be reduced to some extent by what assets they did have.
The term itself is closely related to other uses of the word equity: the value of the owner's stake in an asset, after deducting debt. In this case it is the capital structure of a single asset (rather than a company).