You entered the quotation marks wrong, I fixed it, maybe it will help:
add_filter( 'term_description', 'do_shortcode' );
add_filter( 'category_description', 'do_shortcode' );
add_filter( 'post_tag_description', 'do_shortcode' );
function my_shortcode()
{
ob_start();
require_once(get_template_directory() . '/html/htmlcontent.php');
$content = ob_get_contents();
ob_end_clean();
return $content;
}
add_shortcode("shortcode","my_shortcode");