You can turn the car in early, but it will be considered an early lease termination. You will be responsible for the difference in the residual value as calculated under the lease agreement vs. the price they can get for it at auction.
Generally, it is much, much better to hold out until the end of your lease. At that point, the leasing company has to eat any difference between what they calculated as the likely residual value at the end of the lease, and what they can get at auction in the current market. They took on that risk as part of the lease, but ONLY if you run the lease to it's end.
However, if you are really determined to get rid of the vehicle, call your leasing company to figure out what it will cost you. The calculations are complicated. But if the car has held value better than was expected when you first got it (as some used cars have done), then you might be able to get out of it at no cost. The financing company will generally sell the car at auction, so the value they get for it will be much lower than what you see similar cars selling for on car lots. (While you may turn the car back into the dealer you got it from, they aren't the owners and don't resell it - they just hold it until the leasing company comes to pick it up. Sometimes the dealer may chose to buy it from the leasing company - again, at auction prices - if they think they can make a higher profit flipping it vs. other used cars they may be offered, but that's not a given, and you don't get any increased value from it.)
And for those guys where the dealership convinces them to come and get a new car early, well, the dealers are just writing the costs involved with the early termination into the new lease agreement, or covering it by not giving you as low a price on the car as you would get otherwise. Dealers don't give stuff away for free. (For those that don't know, you can negotiate the price of a car if you are leasing it just like you are buying it - the lower the price, the lower your monthly lease payment).