It is simply a managed service that lets you hook devices up to an overlay network, in which they can communicate easily with each other just as though they were on a LAN even if they are far apart.
For example, if you have a server you'd like to be able to SSH into on your home network, but you don't want to expose it to the internet, you can add both it and your laptop to a Tailscale network and then your laptop can connect directly to it over the Tailscale network no different than if you were at home.