IP2 is a very small, free and portable application designed to display your LAN and WAN IP address. If a computer is directly connected to the internet then the LAN and WAN IP address might be the same. However, if the computer is behind a hardware router or filewall then there will most likely be two IP addresses. One is the internal IP address (something like 192.168.0.2 or 10.1.1.2) and the other is the external, internet assessable IP address that your ISP provides you (something like 126.96.36.199). The reason why you would need to know your external IP address is if you want someone else to connect to the computer via the internet. A common use for this is if you are running a server on that computer (web server, game server etc..).
IP2 provides an easy way to find out the external internet IP address. IP2 goes through a list of IP checking sites (checkip.dyndns.org, whatismyipaddress.org, ipchicken.com and a few others) and displays the IP address from the first one that replies.