Broadband basically works through a "signal" from your local exchange which is sent down the copper wire used for voice calls.  The copper wire sends the signal in analog form, this needs to be converted to digital so that the computer can understand the data, this is done with a modem (modulator-demodulator).  In recent years routers have modems built in to offer several features in one device, however modems are still sold and used in many cases.

When connecting to the Internet the modem/router must see the signal sent from the exchange to be able to communicate with other network devices, an image will been drawn below to illustrate the full steps involved when connecting to the service.