You'll need to access the calibre server via your external IP address (
Google: what is my ip).
Are you behind a router? In that case, you're also going to need to learn how to set port forwarding for your router.
Since home internet connections tend to have dynamic/changing IP addresses, you might want to sign up for an account from one of the dynamic DNS services (e.g.
http://www.no-ip.com/). That way, instead of using something like
http://74.125.224.72/ you can use
http://myname.no-ip.com/.