Drupal Database or MySQL Databse
As of Drupal 7, MySQL, PostgreSQL, and SQLite data types are supported in Drupal core. 

Any web hosting company will offer at least one database server.

Basically: 


you will copy the drupal files to your server via an FTP client
you will create a database from your web hosting company admin panel
you will go to www.yourwebsite.com/install.php and while installing Drupal you will provide the database credentials 
done


You can find more info about creating your database here:

https://www.drupal.org/docs/7/installing-drupal-7/step-2-create-the-database