It could really mean any number of things…
First, and I assume you’ve created a database already via the control panel, have you given permissions to the user trying to access your mysql database?
I’m also not sure you can connect to just the mysql server, without specifying which database it is you wish to use.
Considering you can specify which host(s) are allowed to connect and such anyways, it would only make sense. Though I’ve never tried to get a list of all my databases with one of my limited accounts, so it might be something worth looking into
Other than that, the only thing I can really think of is that your database server might have been down at the time.
It does happen occasionally, though very infrequently in my experiences thus far.