You owe more than your car is worth.

Usually because you had a very long loan (6, 7, or 8 years)

And/or your interest rate is very high

Your car depreciated faster than what you owe.

Beware of this one.  Remember, nothing is free.

Whatever you may still owe on your current car after trade-in will be ADDED to your new loan.  

YOU WILL OWE MORE.

Dealer Invoice. It is the price paid by the dealer to the manufacturer for the vehicle.  Dealers often pay less than what the invoice indicates, but use this as the bottom price

 A high-profit product sold by the dealer that potentially covers repairs or service beyond the duration of the vehicle's factory warranty.  Like an extended warranty, it is generally a poor value for a buyer. 

 A slang term (also called being "under water") for Negative Equity.  

 These are usually cash-back rebate offers or low loan interest rates from the automaker straight to the consumer. That is, a consumer must request the incentives be applied during negotiations.