Briefly,
1)Your router gives your wifi device a local address, 192...., 127..... or 10...., (unless you set a static address that must be the same local network) and you set your port number on your wifi device to listen on and/or send recieve.
2)Log on to router and add a setting in 'port forwarding' to direct recieved (from internet) request with port number of your device to go to your local address of your device.
3)now, if your PIC simply, continously ser-out's stuff, and you can place wifi device to tcp-listen mode, HyperTerminal can connect and continously display your data until closed.
4) you can connect locally as you said you did, and ...... use 'WHO AM i' web site to get your Internet Service Providers given address to connect to your device the same way from the internet.

don