A covenant is a promise in a contract or contract-like legal agreement. For example, lease agreements include covenants to pay rent.
Definition from Nolo’s Plain-English Law Dictionary
An agreement, contract, or written promise between two parties that constitutes a pledge to do or refrain from doing something. In the case of real property, covenants are found in deeds or in documents that bind everyone who owns land in a particular development. (See also: covenants, conditions, and restrictions)