my two cents:
routers simple re-route data from one network to another. Its like a barrier. the internet on one side (your cable modem) connected to the Wide Area Network (WAN) port on the router and your computer(s) on the otherside, the Local Area Network(LAN) ports.
I think most people want a router because they have more than one computer and want to have a internet connection for all of them. The software builtin to the router (NAT) provides for this. the router assigns each computer a internal IP.
Routers can also be a good security investement and are inexpensive. How:
You have one external IP address provided by your ISP and each computer is assigned a non-routable internal IP address.
a router that has SPI (internal firewall) will drop any unsolicited internet traffic.
thats all good for external traffic. a better idea would be to use a software firewall (and a router) on each computer for outbound traffic. A router wont do much good for any malware that you get on your computer like say via a email attachment. A software firewall will alert you to outbound connections.
its like: router=inbound security, software firewall= outbound security
