Whilst No Man's Sky did not start its life as a multi-player game (in-fact it was designed to be lonely); it has evolved to include a great deal of multi-player elements.
Players can naturally encounter each other in the wild (called Ambient multi-player).
They can also do missions together from the Space Anomaly's Nexus in groups of up to four, choosing from the 16 players there.
Finally, with the use of a friend code, players can join each other's games, bringing their own progress in with them.
Players can explore together & build together. They can fight cooperatively or PvP, should they adjust their settings accordingly.
With Expedition mode, all players follow the same route & therefore have a much greater chance of running into other players in the wild (you'd struggle not to).