Many people do not realize that there is a difference between broadband and WiFi incorrectly believing they are one and the same.
Broadband provides high bandwidth access to the internet through a variety of methods, copper telephone lines, fibre optic cable (a la Virgin Media), via wireless (not WiFi) networks using 3G or 4G (the same as your smart phone) and even via satellite. Computer devices then access this connection either via a physical wired connection or via WiFi connection.
If your computer only has a wired connection it comes with the limitation that you work from one fixed point. WiFi enabled computers (laptops, smart phones and tablets) allow you to expand your working area. It is possible to have a WiFi enable network within an area that does not have a broadband connection.
These days most internet service providers (ISPs) will provide a wireless broadband modem to access their service, and such a unit actually contains several different elements:
This is the part of the unit that provides the connection to the internet.
The device that handles the exchange of data between the broadband modem and the computers, and the local networking from computer to computer connected to the same router/network hub.
Provides a method of connection via a physical cable to the router/network hub and via it to the internet. A non-functioning broadband connection does not stop computers connected via a wired connection from accessing the local network.
Provides a method of connection via wireless to the router/network hub and via it to the internet. A non-functioning broadband connection does not stop computers connected via a WiFi connection from accessing the local network.