To understand a private network you must understand a public network. A public network is available to everyone and usually has access to the Internet, ie a wireless network in a coffee shop as anyone can connect to this.
At Nimbus Hosting our public network is the physical network between our servers and our public Internet routers. This network uses public IP addresses like 188.8.131.52.
Private networks are local networks that sit behind dedicated or cloud hosting servers and access is restricted and tightly controlled for example with corporate networks or networks within schools where privacy and security of files and databases is essential.
These networks are usually connected at high speed, either 1GB or 10GB, to allow fast data transfer between services. These services might be applications talking to databases or caching systems like memcache or redis. Alternatively they might be used for backup data or management networks.
Private networks usually use a different physical network port on the back of a server to separate the traffic from public network traffic.
Private networks are secure, although not usually encrypted, because they use private IP addresses like 192.168.x.x or 10.x.x.x that cannot be routed over the Internet.
A server will work out whether to use a private or public network depending on the IP address that it needs to connect to and the default gateway. The default gateway will be assigned to the public network port and is used to route traffic to the public Internet.
At Nimbus some of our dedicated server customers use private networks to separate their web and database servers to give them more capacity and improve performance. Generally applications will transfer much higher quantities of traffic between the database server than with the end user visiting their web site or using their application.
We also use private networks on our Cloud, VPS packages and on our switches for management traffic. We use this private network to access a server or switch should the public network port become overloaded.