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/