A covenant is an agreement. You will sometimes see the phrase "restrictive covenant" used in housing information. A restrictive covenant is an agreement which places restrictions on how land can be used. You could, for example, be restricted from redeeming the ground rent on your property if there is a restrictive covenant to this effect in your lease.
The word is sometimes used as a verb in a tenancy agreement. A tenancy agreement might read "The landlord covenants to pay all rates due on the property". This simply means that the landlord agrees to pay the rates on the property.