writing an unique php function to be used on my website

You are returning the translation in your function, not printing it. Using <?php echo date_translation(); ?> should solve the problem.

(given that functions.php is initiated at the time you use the function)

Edit: In order to follow WordPress convention, you should call the function get_date_translation(). If you want the function to echo the result instead, you should call it the_date_translation()