The app will work from outside your network, but the IP address does change and it's not going to work unless you configure port forwarding in your router. This is fairly easy, however you will need a static IP (or use a [free] DDNS service, like dyndns).
However,I would strongly recommend that you use a VPN instead of just opening the port as it is much more secure (and will also let you use many other network programs as well). This can be difficult, however there are many tutorials on setting up VPNs on Linux systems (Windows is slightly different, may be harder). Google for OpenVPN if you're intereseted.