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First please read this page https://www.akeeba.com/documentation/akeeba-backup-documentation/restoring-backups.html#general-guidelines 

Then read https://www.akeeba.com/documentation/akeeba-backup-documentation/restore-backup-archives.html

As you see, Kickstart only extracts the backup archive. The database dump along with the restoration script (which restores the database and reconfigures your site) are included in the backup archive at backup time. 

If you are restoring on the exact same site (on the exact same server, domain/subdomain and directory) you backed up from you don't need anything else. The database connection information is already known to the restoration script and you basically just click next until the restoration is over.

If you are restoring to a different site or server or domain or directory you will need to supply the database connection information. You either get this information from your host or when creating a database yourself. Remember, this is only necessary if you are restoring somewhere else than where you backed up from.

You never need to edit any configuration files to use our web software. The restoration script has an interface which guides you through the restoration process and lets you enter the database connection information i.e. host name, database name, username and password.

I think it's best if you watch the whole process as a narrated video: https://www.akeeba.com/videos/1212-akeeba-backup/1618-abtc04-restore-site-new-server.html