When you want to access the Internet from one of your computers,
the router looks at the location that you've requested and recognizes
that it's a request for a computer that's not part of your home network.
So it passes the request on to your Internet Service Provider through
whichever kind of Internet connection you've chosen. Cable modems
and DSL modems are the two most common high-speed Internet connections
available for home users, though ISDN and satellite wireless connections
are also available. Your Internet connection device is different than
your router.
Most Internet connection devices use either Ethernet cables or USB
cables to connect to your router (or to a single computer in your
house). The difference is in what sort of cable (if any) they use
to connect to the Internet.
56K dialup, ISDN, and DSL modems use telephone cable; cable modems
use coaxial cable, the same sort that your television uses; and satellite
wireless connections may use a wire that runs inside your house from
an antenna or dish, but the connection from your house to the service
provider is made through radio-frequency airwaves.
In any case, though, you can use an Ethernet cable or USB cable to
connect your router to the service provider's equipment, and most
service providers will help you set up the connection from their equipment
to their system.