LOCAL credentials are simply a map between a user's User ID number and NIS+ principal name which includes their home domain name. When users log in, the system looks up their LOCAL credential, which identifies their home domain where their DES credential is stored. The system uses that information to get the user's DES credential information.
When users log in to a remote domain, those requests use their LOCAL credential which points back to their home domain; NIS+ then queries the user's home domain for that user's DES credential information. This allows a user to be authenticated in a remote domain even though the user's DES credential information is not stored in that domain.
LOCAL credential information can be stored in any domain. In fact, in order to log into a remote domain and be authenticated, a client user must have a LOCAL credential in the cred table of the remote domain. If a user does not have a LOCAL credential in a remote domain the user is trying to access, NIS+ will be unable to locate the user's home domain to obtain the user's DES credential. In such a case the user would not be authenticated and would be placed in the nobody class.