When you enter the world there will be other player sharing the space, but it's not necessarily all the players in the game or server. You're free to work together with these other players or go off hunting on your own, though there will occasionally be public events that encourage you to lend a hand as they are practically impossible alone. What the game loses in some functionality it makes up for in cutting out some of the complexity, and Destiny is handling all the details of behind the scenes making it more ideal for the jump-in and jump-out nature of consoles. Want to get a team together to tackle a mission? Destiny can match you up quickly and get you into the action.
It manages to capture that secret sauce of letting you solo on your own but while still feeling connected to other players. If you see someone in trouble you can run over and revive them, finish off that tough opponent together and then simply go your separate ways without needing to jump through a bunch of mechanical hoops or loading screens. Granted, the game is a lot more fun when you're in a fireteam with a few of your friends.