There are a few different "IPs" to concern yourself with. I'll list them, and explain them as best as I can:
127.0.0.1: This IP will ALWAYS be the same IP pointing to the computer you are on. This will NEVER change (well, it might someday if we decide to change the way TCP/IP works, but don't worry about that).
Your internal IP: In almost all cases, you are connecting your computer to the internet through a modem (commonly also called an internet gateway). This decide (or another device down the line called a router) will give you an IP that usually starts with 192.168 and then will have two more digits, such as .1.100 (192.168.1.100). This is your internal IP (also called your NAT IP, etc) and will work for anyone on the same internal network as you. This will NOT work for anyone NOT on your network.
Your external IP: This will be the IP given to your modem, and can usually be found by going to
http://whatismyip.com/. This IP will work for people external to your network, but ports need to be opened and properly pointing to your internal IP on the modem.