How to show the archive / post type description on Single templates

Within the loop, you can do it this way, outside of the loop, pass the post ID to get_post_type function. :

// Within the loop
$cpt = get_post_type_object(get_post_type());

if($cpt !== NULL)
{
    echo $cpt->name;
    echo $cpt->description;
}

If you need to see more about get_post_type_object you can find it in codex.