3 Answers

Check here   >http://www.lease2purchase.com/what-is-a-lease-purchase-contract.php

It kinda depends on what you are talking about. 
For a house, you can "rent" it for a period of time with an option to buy.  At the end of the "rental" period, should you decide to purchase the home, a portion of the "rent" is applied toward the purchase price.
For stuff you rent from a place like "Rent A Center", I think it would be very similar.  A portion of your rent of the couch or washer or bedroom furniture is applied toward the purchase price. You are probably paying interest on top of that, but I don't know for sure.
With an automobile, you lease for 36 months and pay (usually) over $2000 just to get the keys and drive it off the lot.  You pay a monthly lease amount (somewhere in the neighborhood of what a car payment might be) and need to insure and register the vehicle.  At the end of the lease, the mileage over an agreed upon amount (usually 36,000) must be paid at some pre-determined amount per mile (so be careful about driving too much or too far).  You have, at that time, the option of purchasing the vehicle (and it's a lot of money) or you can just leave. You could also lease another vehicle at that time (or later).

SOOOOO, hopefully that helps.  

Definition of lease purchase. Lease contact under  which a portion of the lease payment or rent is applied to the purchase price of the lease asset or property.