Capitalized Cost (Cap Cost) - The price you agree to pay for the car. Compare it with the MSRP, or sticker price. The capitalized cost should be much lower. In fact, it should be closer to the "invoice price," which is, in theory at least, what the dealer paid the manufacturer for the car. Your down payment and trade-in should reduce the capitalized cost; if they don't, there's a problem. Also, points you've earned from the manufacturer's affinity credit card apply to the cap cost.
Capitalized Cost Reduction - Your down payment by another name.
Depreciation - The wear and tear you inflict on the car while it is in your possession. Mathematically, it is the difference between the capitalized cost and the car's value at the end of the lease.
Downstroke - Everything you have to pay the day you sign the lease, including any down payment, fees and taxes.
Gap Coverage - Extra insurance the leasing company provides to cover you if your car is ever wrecked or stolen. The gap is the difference between how much it would cost to replace your car and the amount you would have to pay the leasing company to get out of your lease. The captive finance companies (like GMAC and Ford Motor Credit) tend to include it for free. Other companies might try to charge you, but see if you can get them to throw it in for free.
Invoice Price (Factory Invoice) - This is roughly what the dealer paid for the car. Use this number as a benchmark to figure out how much you should pay.
Manufacturer's Suggested Retail Price (MSRP) - The sticker price. Nobody should pay even close to this much for a car.
Money Factor - This figure is used to calculate the portion of the monthly payment that goes toward paying interest. It is expressed as a very small number derived from the interest rate. Multiply by 24 to convert it to a regular interest rate. For example, a money factor of .0040 equals a 9.6% rate.
Residual Value - The predicted value of the car at the end of the lease. You agree on this value before the lease is signed. It's what you would pay if you decide to buy the car when the lease is up. It's often expressed as a percentage of MSRP.
Subsidies - Incentives or guarantees given to dealers, usually in order to boost a car's residual value and/or cut interest rates (and thus reduce your monthly payments). A lease with subsidies is also called a "subvented" lease.
Walk Up - A classic sales strategy wherein a salesperson lures you with a low base price and then "walks up" the dealership's profit by selling you a lot of options.