It's a space exploration game-that in the trailer at least-you were promised varied planets full of strange and varied flora and fauna-the trailer showed a river with dinosaur-like creatures and vivid trees and plants, and other people who were there to explore, or trade, or sight-see.
The problem was that most of that did not exist when you started the game. You usually ended up on very barren flat toxic, irradiated or too hot or too cold world-often without water. The story was you were an explorer with a broken-down spaceship/explorer. You wake up from a crash-landing and set out to explore the world to complete the first few quests to get your spaceship back in spaceworthy condition and move further into the galaxy-where supposedly worlds like the trailer existed, and you'd run into other players.
There are three (now four with the latest patch) alien races you encounter over time, and in theory you learn their languages as you go, and find out their history and a central mystery concerning something called Atlas. Problem was that there was not a whole lot of story behind the aliens (there's more now). And all those other players you could meet? Very rarely happened and couldn't do much together if you did.
There was supposed to be a Minecraft-like element to the game where you could have a base (which was hard to get back to) build technology and do things like farm, but again at the beginning there were just the bare bones of it. Etcetera.
Now I think the game is a lot closer to the things promised in that first trailer. There's a mission/quest system and three guilds you can gain favor with (and then more advanced quests). You can settled down on a world and farm and mine and ignore the whole Atlas mystery if you want. The beginnings of true multiplayer have begun with the latest patch with the promise of more to come. It's fairly easy to get back to your base now. Different and often bizarre looking creatures are found sooner in your explorations, etc. Check out You-Tube for Let's Plays using the new patch. I'm currently watching CheckPoint's Let's Play there.
Original trailer:
No Man’s Sky - Launch Trailer | PS4 - YouTube
This is the trailer for the new patch:
No Man's Sky - Atlas Rises - YouTube
It can be played on PC or Playstation. Be warned that the system requirements can be steep on PC. I can't play it due to lack of memory and video-card memory.