For accessing database of website to be used by android you need to create API (Restful or SOAP). This API will expose you the url on which someone hits, will return the required data from database in the form of JSON or XML.
To create API you need to write server side code. Let’s take that you have created website in Java/.Net/PHP then you need to create webservices in Java/.Net/PHP that will access data from database and expose that data onto the url. Suppose your website isthen you can expose to
or you can create subdomain and expose the api on that sub domain. To know how to create webservices /APIs in Java/.Net/PHP please go through google.
If your website is developed on wordpress, opencart and other open source tools then you need to add plugins that will expose API automatically
And on Android side you need to use these API using HTTP request and in response you will get a JSON string or XML String. Then you have to parse that string and show data as per your requirement.