How to add description over forum list on bbpress root page

One possibility would be to hook into the bbp_template_before_forums_index like this:

add_action( 'bbp_template_before_forums_index', 'wpse118937_bbpress_forum_list_desc');
function wpse118937_bbpress_forum_list_desc() {
 //add your description code here
 }

This will be displayed after the breadcrumbs and before the list.

If you want more extensive customizations you can customize the template for that, but you shouldn’t do that in the plugin folder directly, because this will be overridden on updates. So before you can change your the according template file you have to do this:

To customize bbPress:
The directory “wp-content/plugins/bbpress/templates/default/” contains the
directories “bbpress”, “css”, “extras”, and “js”, and the file
“bbpress-functions.php”.

  • The “bbpress” directory contains template parts. Copy any of them into a directory named “bbpress” in your themes root, so it looks
    like: /wp-content/themes/%your-theme%/bbpress/
  • The “extras” directory contains optional root level page templates, to make life a little easier when customizing; copy any you
    want to use or modify into the root of your theme. eg.
    /wp-content/themes/%your-theme%/
  • The “css” directory contains style sheets that work with the default markup. Copy any you want to modify into a directory named
    “css” in your theme’s root. eg. /wp-content/themes/%your-theme%/css/
  • Basically, you could copy the entire ‘bbpress’ and ‘css’ directories out of bbPress’s default template directory, and into your
    theme, and bbPress will use the ones located inside your theme
    instead. Pretty neat, eh?

Source: http://codex.bbpress.org/theme-compatibility/

The template file responsible for showing the forum list is content-archive-forum.php.