You stated the obvious. ;-)
The IP# in your SysPrefs is the local IP# of your computer in the LAN. (Thounds of computers have excatly this IP# on their local network.) When you log into internet, your provider transmits a single WAN-IP# for your net, i.g. t"the router". Let's say 188.8.131.52.
When somebody tries to access your web-sites, this request is sent to the router with the WAN IP# 184.108.40.206. But there is no Apache running on your router, so he will get no response. You have to configure your router that way, that an access on the http-port (80) will be routed to the local computer with the local IP# 192.168.0.10. For this purpose the router has soe settings, usually labeled "routing", "virtual servers", "NAT" or something like this – depends on the router.