From The Apple Wiki

DSID or Directory Services Identifier is a method of identifying AppleID accounts. It is an equivalent to a serial number for a device, however it is assigned to an AppleID or iCloud account for use in identifying cases in iLog, the iCloud support tool, or for verifying a customer over the line.

Every account has an assigned DSID, and provided the customer can verify themselves as the account holder, is available for customer reference.

DSID directly stands for Directory (Service/Storage) Identification.