wp_list_categories to show list of categories and the description

i think that wp_list_categories show categories already formated with <li> tags and you should try using get_categories which leaves the display to you. eg show list of categories and the description

$all_categories=get_categories();
echo "<ul>";
foreach($all_categories as $categories_item)
{
  echo "<li>".$categories_item->description."</li>";//you get the idea
}
echo "</ul>";

EDIT: i saw exactly what you need here