Read more here: https://www.gnu.org/software/emacs/manual/html_node/emacs/Directory-Variables.html

The server-auth-dir is where Emacs stores authentication files for Emacs
servers (running over TCP). These are (usually) ephemeral in nature, and
should be ignored.

When working with multifile LaTeX-documents in AUCTeX in emacs, it creates the auto-folder to keep track of styles, macros etc. in the whole document. Unnecessary of versioning purposes.

Reftex adds these for internal processing, only auxillary files for composition and compilation of tex-documents.

Org-mode stores archived TODOs from todo.org into todo.org_archive. It also
creates .org-id-locations in some cases.

The behavior is documented in [1].
The prefix doesn't seem to be documented, but it is hardoced as described in [2].

[1]: http://www.gnu.org/software/emacs/manual/html_node/emacs/Interlocking.html#Interlocking
[2]: http://tekman.livejournal.com/79598.html