What people usually mean by 'full coverage' is comprehensive and collision coverage. Comprehensive coverage will cover your vehicle for losses resulting from incidents other than collision, like if the car is stolen. Collision will cover your vehicle for damage sustained when your car hits or is hit by another vehicle or object. If you are financing your vehicle the lienholder usually requests this type of coverage to be on the vehicle.

Loan/Lease GAP insurance provides extra coverage to you during the first few years of you owning your vehicle. With GAP if a loss occurs this insurance will pay the difference between the actual cash value, which is what your 'full coverage' insurance will payout, and the current outstanding balance of your loan or lease. Without GAP insurance you would end up paying this difference yourself.