How can I show some description in the “All Posts” view of a custom post type in Dashboard?

The filter views_{$this->screen->id} is fired just after the title of post edit screen has been print to screen, so it’s a safe place to just echo what you want.

So you can simply check here:

function post_type_desc( $views ){    
    printf('<h4>%s</h4>', __('Your description here.') ); // echo 
    return $views; // return original input unchanged
}
add_filter("views_edit-POST_TYPE_HERE", 'post_type_desc');

Replace your_post_type here in POST_TYPE_HERE.

Hope this will help you.