IP connections must be established between routers with public IP addresses in order to link networks via the Internet. These routers provide the connections between multiple subnetworks. When a computer sends a packet to a private IP address in a remote network segment, the local router forwards the packet to the router of the remote network segment via the Internet.
The "encapsulation" of data packets with private IP addresses inside packets with public IP addresses is handled by the VPN gateway. Without VPN, computers without public IP addresses would not be able to communicate with one another via the Internet.
