A covenant, is a solemn agreement or promise to do or not to do something. There are various different ways the word is used.
In land law, there are special types of covenant which ‘run with the land’ . These are enforceable by or against anyone who owns the land – not just the person who made it in the first place.
This type of covenant has to relate to the use of the land in some way. For example a covenant not build on a specific area of land or only to use it for a specific purpose.
The word is also used sometimes to mean a special sort of agreement, created under seal which can be enforced without ‘consideration’ (see here for an explanation of consideration).
In the world of landlord and tenant people tend to be less technical and the word covenant generally means a clause in the tenancy agreement (or possibliy implied into the tenancy agreement) such as the covenant of quiet enjoyment.
So if you are puzzled by references to ‘covenants’, think formal agreement to do or not to do something.