I am copying an answer from Microsoft Answers as it answered the question much clearer than I could explain.
Private network or home networks are when you know and trust the
people and devices on the network. Computers on a home network can
belong to a HomeGroup. Network discovery is turned on for home
networks, which allows you to see other computers and devices on the
network and allows other network users to see your computer.
Public network are for the networks in public places (such as coffee
shops or airports). This location is designed to keep your computer
from being visible to other computers around you and to help protect
your computer from any malicious software from the Internet. HomeGroup
is not available on public networks, and network discovery is turned
off. You should also choose this option if you're connected directly
to the Internet without using a router, or if you have a mobile
I would like to inform you that system network configuration does not
come configured with a network. You have to configure it when you
connect to the Internet connection for the first time. When
configuring the network connection to the system it might have got
selected to public network. However, you can change Public network to
Home network from sharing center.
- Go to settings and click on Network & Internet.
- Click on Wi-Fi on the left pane, and click on the Manage known networks.
- Click on the wireless network connected you want to manage and click on Properties.
- Now turn on Make this PC discoverable.
A point missing about the public network option is that sharing services SMB, etc.. should be disabled and open ports will be greatly limit. Less open ports result in fewer attack vectors. So, choosing public network when you are using an untrusted network is much wiser.
Why is the default to allow public networks, and disallow private
This is likely because most non-technical users will select the default option, which is likely safer.