if you want the description to display right when the item is selected then you must do that with javascript, cannot be done with PHP. if you want to display the description after the form has been submitted then do something like:
if ($_POST['select_box'] == '1') {echo 'this is a description of option 1';}
if ($_POST['select_box'] == '2') {echo 'this is a description of option 2';}
if ($_POST['select_box'] == '3') {echo 'this is a description of option 3';}
// etc...
or better yet, store the description in the database and pull it out based on the form data