Leaving a remote SQL database server with public interface open, especially accessible by multiple Android clients, is probably not advisable because it may have security implications. In this instance, I would usually write a web service that accepted the database objects in XML or JSON form and then write them to the database.
There are many libraries for both web service creation and database CRUD operations for many languages, but I'm not sure which language you're planning to use on the remote web application (if any). Depending on the language you're using for the remote web application, you may be able to find a library that will create a web service and write values to the database all-in-one. Otherwise, you can get libraries for both web service creation and database operations and integrate them together.