To be able to remotely access your MySQL databases, you have to allow access to the databases from your computer. To do so, visit whatismyip.com, and copy your IP address. Then, log in to cPanel, go to MySQL Databases and add your IP to the list of allowed hosts.
The details to use for connecting to the database are:
MySQL Username: [same as cPanel username]
MySQL Password: [same as cPanel password]
MySQL Host: yourdomain.com OR servername.com OR server.I.P.address
(these can be found in the Manage Accounts section in your customer area on siteground.com)