OK, so what is a router? That thing Uncle Stanley had in his wood shop?
Well ... no. True, that's one kind of router. But we're talking about a different kind of router ... a network router!
A network router (sometimes referred to as a gateway) is the box that shares (or forwards) the internet connection from your cable modem or your DSL modem to one or more of your home computers.
Generally, routers come in two basic flavors: wired and wireless. They connect directly to your modem via an ethernet (or CAT-5) cable, and in turn, "route" this connection to your various computers. A wired router connects to your computer by means of another ethernet cable. The wireless variety connects, well, wirelessly!
A router prepares the Internet data so it can be shared by several computers. But there also has to be a way to physically share the Internet service, too. In other words, you need to be able to physically plug in the additional computers so they can share this data. Most network routers do that too, by providing several ports, or places to connect computers, on the back panel. A network router is kind of like a power strip for your home network ... it enables every computer in the house to share one modem.
Of course, if your computers connect wirelessly, then the number of ports your router has on its back panel is moot, since no cables are needed.
What if you only have one computer? Do you still need a network router? Yes, you should strongly consider having one, even with one computer. First of all, you have more than one device that needs to connect to your network: you have your Slingbox! That makes (at least) two devices right there.
Just as importantly, home network routers usually also have a firewall built in. A firewall provides a defense for your computer against intrusion. If your router is handling firewall duties, your computer's operating system usually doesn't have to, which can often be helpful.
Now, having read the Quick Start Guide that came with your Slingbox (you have read it, right?) you already know that your Slingbox also connects to the router via ethernet. Together, your cable modem, router, computers, cables, and Slingbox make up what is referred to as your home network. | 
