The admin console is found at /admin/console/. There is a reference to its commands. Fu has put together some useful greasemonkey scripts, some of which are relevant to console use, especially on the support boards.
Site administrators and others who have been granted privs can use the admin console. Regular users can also use the admin console to perform some tasks as an alternative to a GUI method, or if no GUI method exists. (One of the development tasks: make sure there are GUI methods for all admin console tasks.)