A rebate is a reduction in cost that is refunded to you by the manufacturer after the purchase. But if you don't factor the rebate into the down payment and total price, you will have to finance the amount of the rebate, and you will be paying it back over the life of the loan.
The dealer can also get an additional rebate that is not generally known to the public. If you are aware of the dealer rebate, you can use this fact to lower your cost.
An incentive is an offer that reduces the purchase price or finance interest rate. The incentive will sometimes have a hook like "$2,500 for a first-time buyer or new college grad," or "Get $5,000 in factory cash." These are all incentives to get you to buy now and reduce the price at the time of purchase.