Show terms with matching descriptions.

// Paste into your search page.

if (array_key_exists('s', $_REQUEST) && $_REQUEST['s']) {
    global $wpdb;
    $s = array_map(function($e) { return esc_sql($e); },
        explode(' ', urldecode($_REQUEST['s']))
    );
    $s = '(description LIKE "%'.implode('%" OR description LIKE "%', $s).'%")';
    $res = $wpdb->get_results(sprintf('SELECT * FROM %s a INNER JOIN %s b ON b.term_id = a.term_id
WHERE %s GROUP BY a.term_id',
        $wpdb->term_taxonomy,
        $wpdb->terms,
        $s
    ));

    if ($res) {
        echo '<pre>'.var_export($res,true).'</pre>';
    }
}