A Router is a usually a device, but can be a piece of software running on a computer, that transmits data between two networks that without the router, would not know how to communicate with each other.

When a computer needs to send data to a destination which is not parts of its same network of computers, the sending computer transmits that data to a router. When the router receives that data it then looks at a table of possible routers that it knows about and forwards the data to the router it feels would be best suited to deliver the data to its ultimate destination.

For home users, a router is a device that you would plug your cable or dsl modem into the back of, and connect your computer to. This router would then enable you to have a small network of computers at home that would share the same Internet Connection. The theory discussed above would still apply to this scenario. When one of your home computers send information to a computer that is not on your home network, it will send that data to your router. Your router will receive that data and look at its table of known routers to send the data to. As it only know the router for your ISP, it will forward that data on to them.