The term local directory is really a general way of describing the role performed by an on-premise or domain directory service: the directory service is a database of everything in an Active Directory domain, namely users, devices and resources.

This contrasts with a cloud directory service, which in the Active Directory sphere would be a domain or domains managed through Microsoft Azure.

The second part of this term, services, can refer either to specific functions offered by the directory service such as authentication or to the existence of a local service account that runs background services without a user being logged in.