This error most probably means that you have not configured your phpBB's database settings properly. Check phpBB's configuration file config.php located in the directory where your forum resides.
Please note that your database names and usernames always begin the following prefix user_ where user stands for your username. For more information about MySQL management check this video tutorial.
Another reason for this error is when your database has been deleted. In this case it would be best to restore it from a backup.
If you have problems with your phpBB forum, ask your host for assistance. SiteGround provides the best phpBB hosting and our support team will do their best to resolve your issue.
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