Most websites need a database (WordPress, shops, forums). Installing an app through Softaculous creates one for you. To create one by hand:

Database and user names always start with your hosting account name, e.g. boostdemo_shop. Enter them like that in your app's configuration.
The phpMyAdmin button on the databases page (or under Extra Features) opens a tool for browsing tables, running SQL and importing or exporting databases. To import a database from your old host: pick the database on the left, open the Import tab and choose the .sql file (a .gz archive works too).
Large databases (several hundred MB) are better moved through a support ticket - we import them on the server.