A lease is a contractual arrangement calling for the lessee (user) to pay the lessor (owner) for use of an asset. Property, buildings and vehicles are common assets that are leased. Industrial or business equipment is also leased.
Broadly put, a lease agreement is a contract between two parties, the lessor and the lessee. The lessor is the legal owner of the asset; the lessee obtains the right to use the asset in return for regular rental payments. The lessee also agrees to abide by various conditions regarding their use of the property or equipment. For example, a person leasing a car may agree that the car will only be used for personal use.
The narrower term rental agreement can be used to describe a lease in which the asset is tangible property. Language used is that the user rents the land or goods let or rented out by the owner. The verb to lease is less precise because it can refer to either of these actions. Examples of a lease for intangible property are use of a computer program (similar to a license, but with different provisions), or use of a radio frequency (such as a contract with a cell-phone provider).
The term rental agreement is also sometimes used to describe a periodic lease agreement (most often a month-to-month lease).