In order to access your MySQL database from a remote computer you need to first tell the server which computers are allowed.
To do this, log in to your cPanel at http://yourdomain.com/cpanel and scroll down to the Databases section.
Click on the 'Remote MySQL' icon
Where it says 'Add Access Host', add your computer's IP address or name.
If you don't know what your computer's IP address is, you can find it by visiting http://aegishosting.co.uk/support/ip.php
If you've got a fixed IP address that doesn't change, then that's all you should need to set up the access host. If you've a dynamic IP address then it may change. You might want to look at adding a fixed IP address with your ISP or use a service such as DynDNS.com to provided a fixed name to use.
The other possibility is you can use a wildcard in the host field. If you put % in the field, ANY computer can access your database server remotely. That's obviously a bit of a security risk so it's not advisable on a permanent basis.
If you can narrow it down to say 123.123.123.% or 123.123.%.% you can limit it to say only computers within your ISP or your company which may be a compromise you can make.
Once that is sorted, you can use yourdomain.com or the shared IP address in your computer's remote MySQL admin tool or access the database from another web application running on another server.
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