A router is a device that is used to connect different networks together.
Routers are computers that have more than one network connection/card in them. This allows you to connect two or more networks together. The router then takes network traffic from one network and puts it on the other network
If you have Internet at your house or business then you will have a router that connects between your network (which could just be one PC) and the Internet (actually to the network of your Internet provider or ISP). The Internet is made up of lots of networks which is where the word Internet comes from. You are communicating between lots of networks. The router is the box that connects your computers to the phone line if using DSL or to the cable wire if using cable. Internet is a shortened word for internetwork.
Different networks use different domain names (i.e. dwightwatt.com, att.net) and different IP addresses (i.e. 192.168.3.0, 172.33.0.0)
The router looks at information (packets) that it receives and decides does it belong on the network it is on or does it belong on another network. If it is ion the network it belongs on the router ignores it. If it belongs on another network the router then sends it out the network interface card that connects to the network it belongs on.