Apparently, the well-known hosting provider GoDaddy allows remote access to MySQL databases, created within its environments. Quoting from the help page:
Direct Database Access allows you to remotely manage your hosting account databases with external tools such as Microsoft SQL Server Management Studio Express and MySQL Query Browser. These tools offer a fast connection to your database(s) and additional functionality for advanced users, however, it is a less secure way to manage your databases.
Most users do not require this functionality and can manage their databases through the tools we provide and the backend provided by the application using the database (e.g. WordPress). If you do not need to access your database using one of these third party tools, then you should not enable Direct Database Access.