As far as I understand it Answerbanker you pay monthly premiums to the leasing company while you use the car. Whenever the car requires servicing or repair that is taken care of by the lease company and the costs covered in your premiums. You are contracted to keep the car for a certain time period, usually three years. After that time you can either return the car to the lease company or have the option of buying it from them for a final payment.
The advantage is that you don't have to worry about breakdowns, servicing, repairs etc. The disadvantages are that you are contracted to keep the car and the payments up for the lease period. If you lose you job or licence you can't return the car and have to maintain the payments. You also have to ensure you keep the service record up to date and present the car for servicing at the correct time intervals.
That's my understanding from other people who have leased vehicles.