Home equity is how much more your home is worth than what you owe on it. Negative equity, also called being underwater or upside down, means you owe more on your mortgage loan than the home is worth. The value of a home changes based on things like supply and demand for real estate and the health of the economy.
Obviously everyone wants equity in their home. If you have enough, you have the option of selling your home for a profit. Negative equity is bad and most homeowners never anticipated having it.