No Man's Sky is largely a sngleplayer experience with a multiplayer element to it. The developers say the galaxy is the same between everyone and that actions of "significance" will be shared. For instance, killing a single bird won't be shared but if an entire species of bird goes extinct than those creatures will blink out of existence for everyone.
Apparently, the game will let players loose in a galaxy filled with alien planets—some Earth-like, some not. Putting the scale of the game into context, Rock, Paper, Shotgun says No Man's Sky may be the first title without a skybox: "If you’re standing on a planet’s surface and look up," the site explains, "every single dot in the sky is an actual star you can go visit."
Activities will include exploration and resource gathering, both in spaceships and on foot. This will be a multiplayer game, and players will be able to share the discovery of new planets with others. But don't expect heated firefights. According to Hello Games' Sean Murray, "[G]enerally people are playing together cooperatively to the benefit of everyone."
Source: The Tech Report