To expand a little bit: it provides an (almost) zero-configuration way to set up a private 'layer 2' network that you can connect your home server to, and any other machines that you want to be able to connect to it or to each other. It handles NAT traversal completely transparently.
In practice, it means that if I have a (say) NFS server connected to a Zerotier network I control, I can connect to it transparently from anywhere from another machine on that network, no matter what NATs / firewalls either machine is behind, even if they change. Perfect for phones, roving laptops, etc. I've gone to a model where I do most of my development (over mosh/tmux) on my home machine, from wherever I happen to be.
No home firewall configuration needed at all.
> ZeroTier’s software is open source and free to use for most purposes including personal use, internal use within a business or academic institution, and evaluation for uses that require commercial licensing.
I was able to find this: https://github.com/zerotier/ZeroTierOne
Also, if you can't open ports outbound at all, there's https://samy.pl/pwnat/ but it makes things very slow.
[0]: https://staaldraad.github.io/2017/04/17/nat-to-nat-with-wire... - you can ignore 'NAT-B' in this one.