A network links devices so they can exchange information. A local network covers a limited place such as a classroom. The internet links many networks. A router forwards data between networks; some home boxes combine a router, switch and Wi-Fi access point.
Worked example
A tablet sends a picture to a printer on the same local network. That local job can work without internet access if the printer and software support local printing. Wi-Fi and internet access are not the same thing.
The Paper Classroom Network
Imagine two tablets and one local printer connected to a classroom's network. A router connects that network to other networks. All three devices have permission to communicate. Draw a line from tablet A to the printer. No real addresses, passwords or network changes are needed.