A more thorough explanation:

demesnial

Demesnial means something that is related to a demesne. A demesne is a piece of land that is owned by a lord or a nobleman.

• The castle's gardens were part of the demesnial land.
• The demesnial rights allowed the lord to hunt on the land.

The examples show how demesnial is used to describe things that are related to a demesne. In the first example, the gardens are part of the land that is owned by the lord. In the second example, the lord has certain rights on the land because he owns it.