This post is a part of an unfinished Appendix from a series of articles on introducing 10-year-olds to programming with the goal of making a simple Minecraft mod.
Before we can talk about the multi-player games, servers, and the internet in general, we need to understand a bit about networks. A network is a group of computers connected together that can "talk" to each other. A very simple network could be two computers connected by a network cable or two Nintendo DSes sharing a game wirelessly.
In most homes today, a lot of electronic devices (computers, laptops, printers, iPhones, DSes, etc.) are connected to a wireless network (also called WiFi). The piece of equipment that provides this network is usually a router or hub. Since routers are more common and multi-purpose, we're going to assume you have one for this article :)
Just like your friends have a phone number you use to call or text them, computers have IP addresses. When a computer joins a network, an input/output hardware device (i.e. network card or USB network adaptor) receives a unique IP address from the router. An example of an IP address on your home network could be 192.168.0.42.
Sometimes we don't need to remember our friends' phone numbers; home and cell phones often have a built-in address book so you can choose someone by name and the phone automatically knows which number to use. Similarly, computers on a network can be identified by name instead of IP address. A special computer program or server called a name server translates a machine name into an address. For instance, I name a lot of my machines after Transformers - the one I'm writing this article on is called 'skyfire'.