For those who don't know about it, it's a spaceflight simulation game. You design a spacecraft from parts, assembling rocket engines, fuel tanks, thrusters, command modules, etc. into a design, and then test it and try to get it into orbit; or from there, to other planetary bodies. Multiple spacecraft if you want: you can dock and coordinate them, or build space stations or moon bases.
It's got an incredible amount of detail, modeling a whole solar system with various planets and moons and asteroids. Remember how the staff working on "No Man's Sky" made claims about how "all other video games are fake, they have a skybox, the planets and sun in our sky are real real and you can fly to them" (claims which turned out to be largely false)? Well, Kerbal Space Program actually delivers on that experience. You can rocket into space, dock in orbit with something you've put up there previously, gravity-slingshot yourself to another planet, parachute a lander down to the surface and roam around, etc.
The game has realistic space flight physics and orbital mechanics (though tuned to be very generous to players compared to real life). You can learn a lot about the basic mechanics of spaceflight just by playing it; you begin to intuitively understand delta-v, apoapsis and when to apply thrust, etc. If you want to dock with with something then you need to plan an appropriate launch window. Maneuvering in orbit is very interesting and initially counter-intuitive (if a spacecraft is "ahead" of you in orbit, in which direction should you boost to "catch up" to it? If you boost directly toward it, you'll increase your orbital speed and thus the shape of your orbit, taking you away from it in a different dimension!). Getting to other astral bodies is tricky and requires more planning. KSP manages to make all of this challenging but fun.
If you'd like to learn more about it, or are even just curious what the fuss is about (the game itself, not the drama), I'd direct you to videos by Scott Manley [1]. Here's a video of a fairly sophisticated mission starting with liftoff from the launch pad, made by another YouTuber [2] (skip to 13:00 to see him planning orbital maneuvers like circularizing his orbit). Manley's "Interstellar Quest" mission has even more complex orbital planning (5:00) [3].
The depth of KSP is astonishing and there's not much else out there like it. It's in the same ballpark as Minecraft in terms of the amazing creative sandbox it provides, with a world that has a ton of depth to explore. There's a wonderful atmospheric feel with the music and artwork that happens when you successfully lift off into space, going from the thrill of launch to the serenity of orbit. It's a beautiful feeling and one that isn't easily captured by recordings.
So it's sad to hear that the company and/or developers who made the game aren't carrying on. The game may not be a commercial success on the scale of Minecraft but the artistic and conceptual achievement are on par or greater.
[1] https://www.youtube.com/user/szyzyg [2] https://youtu.be/RzbDyx4Tpdc?t=10m7s [3] https://www.youtube.com/watch?v=FSzj_uk1fRQ