you must escape the quote:
$today = Date("l F d, Y");
$sqlUpdate = 'UPDATE USER_PROFILE SET
FIRST_NAME =("'.$FIRST_NAME.'"),
LAST_NAME=("'.$LAST_NAME.'"), URL=("'.$URL.'"),
DESCRIPTION= CONCAT_WS(\',\',"'.$today.'","'.$DESCRIPTION.'")
WHERE ID = "'.$GetID.'";';
or you can just make the DESCRIPTION column receive its actual value:
$today = Date("l F d, Y") . $DESCRIPTION;
$sqlUpdate = "
UPDATE USER_PROFILE SET
FIRST_NAME = '$FIRST_NAME'
, LAST_NAME = '$LAST_NAME'
, URL= '$URL'
, DESCRIPTION = '$today'
WHERE
ID = '$GetID'
";