The data of your application is stored in the database, in order to move this to the live site you could create a backup of your database and restore that on the live site. This depends on the database that you are using, when using the mendix cloud make sure your data is stored in a postgres database e.g.
If your database is not compatible you could export the data and import it in the live site with the help of the excel exporter and importer modules fromthe appstore.
The mpk that you created contains the project not the data for the application. If this is what you want to move then create a deplyment package from studio pro, this results in a .mda file that can be uploaded to the cloud environment or on premise service console. When using the mendix cloud moving the app to the live site is just a matter of the option deploy to licensed cloud node or in a free version use the publish button.
Hope this provides you with some guidance on how to move different things to the live site that you have.