Your billing address is the address that the paper copies of your bills are sent. Your shipping address is where you designate your deliverables should be sent to.
Most of the time, these will be the same address, but they don't have to be the same.
To find your current billing and/or shipping address, go to the Fancards app and click the menu button on the top left corner, then select 'Personal Information'. Your address should be listed under this tab.