$args = array('child_of' => 12);
$categories = get_categories($args);
foreach($categories as $category) {
    echo '<p>Category: <a href="' . get_category_link($category->term_id) . '" title="' . sprintf(__("View all posts in %s"), $category->name) . '" ' . '>' . $category->name . '</a></p>';
    echo '<p> Description:' . $category->description . '</p>';
    echo '<p> Post Count: ' . $category->count . '</p>';
}