It's a free VPN client that allows you to create and connect to a private IP network (hosted by Hamachi) that other people with the same Hamachi VPN client can reach (as long as they know the network name and password that you created).
It can be useful to work around firewall issues - especially when 2 people try to log in at once (maybe because that requires both inbound and outbound connections, whereas connecting by yourself only requires an outbound connection).
On the other hand, it's also another overhead and complexity to your setup, and requires everyone connecting to install the Hamachi client, so probably not worth doing unless you have a firewall issue you can't work around any other way. If you get stuck though, it can be a useful (but not infallable) tool for resolving connection issues.