Here's the technical architecture doc: http://open-eid.github.io/
We all have either a credit-card sized chip card with our keys or a similar mobile SIM card which uses SIM applications. Using those we can do basically everything online, be it authentication to private or public services (using PIN1), or digital signatures (using PIN2).
This is also available to anyone in the world, so feel free to apply for your e-resident ID card here: https://e-estonia.com/e-residents/about/
I read on Wikipedia that some of your newspapers have started requiring it to comment on their articles, and I'd be wary of such developments, since they're so easy to justify (even to oneself) and to accept (since it makes authentication even easier than remembering password).
How do you deal with the fact that most sites would like to have your unique, cross-site identifiable key fingerprint?
Apparently it is not used anymore?
Web commentary columns of some Estonian newspapers, most notably Eesti Päevaleht, used to support ID-card based authentication for comments. This approach caused some controversy in the internet community.[3]