Private residence relief: the entity of the dwelling house: appurtenance
Appurtenance, like curtilage, is a legal concept. The curtilage of a house is an area attached to and including the house. CG64245 describes the concept of curtilage.
Appurtenance describes the resulting legal relationship which the buildings within the curtilage have to the main house. So in practice curtilage and appurtenance are two aspects of the same test. A building which is within the curtilage of the main house will be appurtenant to the main house, and a building which is appurtenant to the main house must be in the curtilage of the main house.
A building which is appurtenant to the main house will also pass with it on conveyance without having to be specifically mentioned.