Networks exist where multiple computing devices are connected together. These networks can be connected in various different ways, commonly using ethernet cables, wifi or Bluetooth. Most people have small networks in their homes where WiFi is used to connect the devices together.
Common misconception – WiFi allows devices to connect together, it may or may not in turn allow the devices to access the internet. Just because WiFi is available, this does not automatically mean that the devices can access the internet.
There is an excellent section on BBC Bitesize about networks.