This global variable indicates whether the current user wants to use rich editing interface (by default using TinyMCE) for creating/editing posts and comments. Since WordPress 2.0, the option of rich editing is set per user, which can be accessed by using the checkbox, “Use the visual rich editor when writing”, in Admin Panel->Users->Your Profile.
richedit is set in the functions
get_comment_to_edit($id) in the [wordpress-root-folder]/wp-admin/admin-functions.php. It is set using the function
WordPress defines an additional function
user_can_richedit which, in addition to checking this option, checks whether the browser supports rich editing or not. Plugin developers can use this function, when using the global variable directly it should not noted that unlike lot of others, this global variable is defined as part of the admin functions.
Back to full list of global variables.