When you trade-in you don’t have to worry about selling the vehicle yourself or any of the associated costs (advertising, showing the car, etc). A dealer may offer a price you could not get yourself as an incentive to purchase a new vehicle. If the trade-in has known problems that could plague you later (when the buyer returns complaining), selling the car to the dealer eliminates the bother.
Trading-in a lease car may relieve you of, in the long run, monthly costs you cannot afford. Sometimes people trade in lease vehicles because of poor gas kilometer or lack of practicality. Plus you could qualify for a tax savings when you trade in your vehicle to a dealer that you would not get if sold privately.