A network check checks:
Whether the IP address (address element on the internet) of the internet access you are using has tried at any point in the last few days to connect to a server that is known to be infected. This indicates that a device connected to the network will also be infected.
That the router (the device that allows you to access the internet) cannot be used to reach any services which might pose a potential security risk. This could be used for attackers to take control of the device.