The type of network pertains to the network that you will connect to. The private network pertains to networks that you trust such as your own home network because your device will be visible to all those that are connected on the same network which would probably be your family or anyone that you would allow access to.
On the other hand, the public network pertains to a network that is publicly available such as a library or coffee shop. If you will switch to a public network, your device will be hidden to all other people that are connected to your network.
If you feel that someone was able to access your network the first thing you would have to do is to change your modem's interface or gateway password then after that you would need to change as well the password for your network to make it more secure.