To access your MySQL database, you need a unique hostname (domain name) or IP address for your MySQL server. This hostname can be any name you wish, so long as you have registered it, but it is commonly a subdomain of your primary domain and is named "mysql.example.TLD". For example, let’s say your domain is example.com: you can then create the subdomain "mysql.example.com" which is used to connect to your database server.
This arrangement is convenient to use with DreamHost's MySQL installations, as you can create and manage all of your databases from the (Panel > 'Goodies' > 'MySQL Databases') page.
However, during a server or web host migration, the DNS for "example.tld" may not point to DreamHost's nameservers, so you won't be able to use a subdomain of "example.tld" for the MySQL hostname.
With DreamHost's setup, your MySQL server (which hosts all of your databases) is accessible from any subdomain that you assign to it within your DreamHost account. Thus, you can still access any of your DreamHost-hosted MySQL databases by creating a temporary MySQL subdomain within your panel.