/.HFS+ Private Directory Data is a directory used by the HFS Plus filesystem to implement hard links. Hard links are an expected feature of Unix filesystems, but because HFS+ is inherited from classic Mac OS, the feature had to be implemented in Mac OS X by using this folder as a database of hard-linked files. It is usually hidden from directory listings by the filesystem driver, but may appear when the filesystem is mounted in classic Mac OS, or by a third-party HFS+ driver lacking support for hard links.
The directory is no longer used with the switch to APFS. Devices that are migrated from HFS+ to APFS (upon upgrade to iOS 10.3 or later on 64-bit devices) migrate this data into the filesystem's master file table.
Technically, this is actually named .HFS+ Private Directory Data\r, the \r being a carriage return.
