A covenant is a written promise between a landlord and a tenant, where each promises to do, or not do, certain things.
There are various types of covenants, all of which can be contained within a lease contract. Here are a couple of covenants that might be covered by your rental agreement:
Such covenants are put in place to protect both the tenant and the landlord by setting boundaries and making each party aware of what they can do and what they're entitled to.
Some covenants can be conditional. For example, a tenant may be under covenant to pay rent, but that stands only as long as the landlord maintains a habitable property. Such conditions may vary by state, so make sure you know about lease and covenant laws where you live.