It's been described as the "DIY NASA game", and it features a bunch of crazy little green men called Kerbals as your pilots. Obviously, you need to visit other planets and moons in their star system FOR SCIENCE!
And it is gorgeous...
And those are just some of the smallest images I could find. In my search for those, I found many large, but just damn beautiful screenshots.
Also, as you can probably guess from the one image, quite a lot of humour pervades this game.
But, above all, it is about the self construction and piloting of multi-stage rockets to get probes, artificial satelites, and Kerbals to different oribts, planets, moons, and even assemble bases and space stations. It's a sandbox.
And it isn't even complete yet! They haven't actually got versions of all the possible planets, dwarf planets, and major moons for the Kerbal solar system, nor have they got any asteroids or comets yet, nor have they even finished all of the possible rocket/ship/station/base parts/engines/scientific equipment. But, when you get the paid alpha, it updates whenever a new version with new goodies and fixes come out (and it is by now rather bug-free; usually, bugs in this game surface with major new versions, and are quickly fixed by sub-patches).
And even though those parts are not complete yet, the physics engine is pretty much complete, ironclad, and realistic. You can even simulate gravity in space by judicious creation and operation of a ring space station, though IVA isn't fully implemented yet.
Finally, there is a nice community going on the game's special forums, as well as a handful of great Youtubers with accounts mainly devoted to this game. You can always check out Scott Manley's or HOCgaming's channels for videos of this game.