Basic version is it's a sort of developer focused zero trust network service.

Encrypted overlay network based on wireguard tunnels, with network ACLs based around identity, and with lots of nice quality-of-life features, like DNS that just works and a bunch of other stuff.

(Other stuff = internet egress from your tailscale network ('tailnet') through any chosen node, or feeding inbound traffic from a public IP to a chosen node, SSH tied into the network authentication.

There is also https://github.com/juanfont/headscale - which is a open source implementation of some of tailscale's server side stuff, compatible with the normal tailscale clients.

(And there are clients for a very wide range of stuff).