Website leasing is an agreement between the user (lessee) and the owner (lessor) whereby the privilege of using a website is offered in exchange for regular payments. Website Rental is a similar concept, however often does not always require a fixed agreement.
The idea of website leasing or Rental is for a user to have a website promoting their products or services but not have any overall ownership of the site (in some cases the Domain name can be owned by the lessee or renter). Generally the website owner will charge a monthly or annual fee for this service.
Read more about Website Leasing: Reasons For Leasing A Website