Port forwarding is the answer.
Network Address Translation (NAT) is what allows you to have one public (WAN) IP address and many private (LAN) ip addresses. As your computers initiate network connections to the internet, something like port forwarding is done on the fly. Ports are opened and closed, redirected and reused. Some applications like bittorrent clients, will use Universal Plug and Play (UPnP) to set up a semi-permanent port forwarding that allows external hosts to connect directly to your computer inside your LAN.
Specific services that need permanent open ports need to be manually specified in your router.
The 78... address is public. The idea is that in your router's configuration, you set up port forwarding. There will be a section where you enter the external port, the internal IP address and internal port.
Here is a fuller description of what port forwarding is.
So assuming the socket you want to use opperates on port 3389 (which is microsoft RDP), you set up in the router so that all connections to 22.214.171.124:3389 get directed internally to 192.168.1.100:3389.