Tableau Server works as a team of multiple processes, processors, programs and applications, like data engine, data server, VizQL Server, bacgrounder, application server etc.: http://onlinehelp.tableausoftware.com/v8.3/server/en-us/processes.htm
ServerStatus
Each of those processes generates LOG files with data about user activities, data connections, queries and extractions, errors, views repaintings and interactions, etc.: http://onlinehelp.tableausoftware.com/v8.3/server/en-us/logs_loc.htm
Those data parsed regularly and stored into PostgreSQL-based Tableau Server Administrative Database, called “Workgroup” and also known as Tableau Server Repository.

PostgreSQL Server containing Workgroup DB usually runs on the same Windows Server as Main Tableau Server or (if Tableau Server runs on multimode cluster with Worker Tableau Server(s)) on other Windows Server, which runs Worker Tableau Server and uses non-standard TCP/IP port 8060.

During installation Tableau Server will create the almost empty Workgroup Repository with the main DB Schema called “public”, 100+ tables, 900+ columns (about 100 of them used as Keys), 300+ Joins, 16+ Views and 4 pre-approved users ( 2 internal (repository and rails), 1 SuperAdmin ( tblwgadmin ) and 1 default user ( tableau, which has read-only access to 16 views (click on image to enlarge):
wg82TableauViews
and nothing else). Similar Schema (with linkage between Keys for Tableau 7.0 Repository) is here (Originally published by great Russell Christopher) :
DataDictionary70

None of these pre-approved Workgroup users available outside of Tableau Server environment (unless designated static IP address(es) will be added (this may violate your Tableau License) to pg_hba.conf PostgreSQL configuration file, except “tableau” user (and new default “readonly” user) who can be given a privilege to connect to Workgroup Repository remotely as described here:
http://onlinehelp.tableausoftware.com/current/server/en-us/help.htm#adminview_postgres_access.htm

In November 2014 Tableau Software introduced (Release 8.2.5) a new, 2nd default user, named “readonly” with read access to all Tables and Views of Workgroup Repository: http://www.tableausoftware.com/support/releases/8.2.5

New “readonly” user enables us (if/when migration to Tableau 8.2.5+ or 8.3 happened) to create custom Operational Dashboards and monitor the usage and state of Tableau Server in Enterprise environment. TABADMIN utility’s command DBPASS now has new parameter “—username” which can enable remote access for “readonly default user:

tabadmin dbpass –username readonly p@ssword

Tableau Software also introduced and published the Data Dictionary and Documentation for entire Repository, its DB Schema, Tables, Views and other details here:
http://onlinehelp.tableausoftware.com/samples/en-us/data_dictionary/data_dictionary_8.2.5.html
and here:

http://onlinehelp.tableausoftware.com/current/server/en-us/data_dictionary.html

Please find below the list of all tables, columns, their data types:

Tableau 8.2 Repository: tables and columns

or you can see it here: https://public.tableausoftware.com/profile/andrei5435#!/vizhome/shared/4WQSHR642

and the portion of Diagram of “public” DB Schema for Tableau Server Repository (click on image to enlarge):
wg82L

Russell Christopher originally posted the portion of DB Schema of Tableau Server Repository for v.7.0. here: http://tableaulove.tumblr.com/post/50438516817/better-late-than-never-tableau-7-data-dictionary and then added awesome articles about History Tables in Data Dictionary for v. 8 here: http://tableaulove.tumblr.com/post/50529179435/tableau-server-v8-history-tables and here: http://tableaulove.tumblr.com/post/51220703630/tableau-server-v8-history-tables-part-3-the