It is possible to connect to your MySQL database remotely. First you will need to allow the IP address access, to do this click the Remote MySQL icon in cPanel.
Then enter the IP address or host you wish to allow in the Add Access Host section. % can be used as a wildcard, so the pre-existing entry of 192.168.1.% allows access from all IPs 192.168.1.0-999. Adding a host of just "%" will allow access to absolutely everyone (who knows the password) so this is not advised.
Now you can connect to the domain name on mysql's standard port using the MySQL username and password.