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I don't know what a router is. It mentions Hamachi and the internet.
Hamachi is software designed to create VPNs (virtual private networks).
Hamachi is a program that allows you to create your own secure network of computers connected via the internet, as if they were connected by a single physical local network.
What does this provide?
Hamachi allows you to create a local area network (LAN) over the Internet.
Any applications that work over a local network (Windows File Sharing, Remote Desktop, Remote Assistance, Games) can work over Hamachi networks, and the data transmitted will be protected, and the exchange will be done in a peer-to-peer style.
How does it all work?
Hamachi is a system for organizing virtual secure networks based on the UDP protocol. In such a network, nodes use a third node to establish a connection between themselves, which only helps them find each other, and the information is transmitted directly between the nodes. At the same time, the interacting nodes can be behind a NAT or firewall.