Technologically, it's based on Wireguard. Wireguard is fast; really fast, especially compared to OpenVPN. Using cutting edge cryptography and a new UDP protocol, Wireguard connections feel roughly zero-overhead (they're not, of course.) Connections are peer-to-peer and you usually will get pretty close to the fastest reasonable route between any two devices, whether you're on LAN or overseas, whether there's a strong NAT in front or not.
They've also engineered a lot of things carefully, instead of just cobbling together existing end-user tools in Rube Goldberg arrangements. (Not saying there isn't use of existing code; there totally is. But it's all very nicely integrated from what I can see.) Doing things "the hard way" can lead to more complicated software, but the way they've architected things makes the possibilities for expanding the utility of Tailscale to be nearly limitless. It's also amazingly entertaining to read about. Seriously, just read about how their web browser SSH client works: