A sublease allows the lessee to assign an existing lease to a third party; in this situation the lessee becomes a sublessor contracting with a sublessee (or subtenant). The lessee is simultaneously renting and renting out the same tenement. This arrangement is commonly encountered in commercial properties and less commonly with residential properties.
Many residential, and some commercial, leases forbid the practice. For example, imagine that Bill leases an entire house from Clark, and then subleases the basement to Cody. In this situation, Clark is the lessor, Bill the lessee and sublessor, and Cody the sublessee. Bill remains liable to all of the terms of the original lease while Cody remains liable to only the terms of the sublease.