From what I can tell, it's a space exploration game akin to Space Engine, only where SE was a game centered around the black infinity of space, this game has an entire galaxy of procedurally generated planets that can actually be explored with their own architecture, fauna and flora. There are also survival elements, more info at http://www.no-mans-sky.com/about/
Space Engine isn't really a game. I love how the top comment somehow started with "how could this game have content inappropriate for children" to some giant flamewar about religion.
One of the few games from E3 I really got hyped over. But I'm not following it. I wanna be pleasantly surprised when it comes out
Looks very much like an Elite for consoles. Looks pretty nice, except for the viewing distance, which makes the planets look tiny.