A router is a device that helps route data packets (your media content) between computer networks.

The internet basically requires that every bit of information, media or any other content be broken down to data packets, in order to be transmitted over the Ethernet. These data packets have elaborate headers which help the router decide where, and how to send them.
When you take a broadband connection from an ISP, it usually comes along with a modem and router, to enable you to connect to the rest of the Internet.