At Admin Panel -> Settings -> Switches you have a "show subforums on main page" option. When enabled, each top level forum on the front page of your site has a list of subforums below it. This list of subforums is cached so that they don't slow the page down much. The cache is automatically refreshed when subforums are edited, but if for some reason subforums are altered in a way that doesn't refresh the cache you can refresh it via the regenerate forum option on the edit forum page, or for all forums by regenerating forums at Admin -> Maintenance -> Regenerate.

To change the apperance, edit the HTML between <!-- BEGIN SUBSUB --> and <!-- END SUBSUB --> in your 'front page' and 'show topics in forums' templates (at Admin Panel -> Themes -> Manage Templates). The forum template variables that can be used in this area are restricted to ones which are cached. If you want to use more, use the $subhtmlfields tweak to cache additional fields.