You have a database hosted on a database server (say a mySQL server) and from the Arduino, you want to retrieve data from that database. Is that correct ?
One way to do it is to have a script (say a PHP script) on a web server (say Apache) which, when triggered by calling its URL, retrieves the required data from the database. You call this URL from an Arduino running as web client, and parse it.
Google for "Arduino mySQL PHP" for possible examples.