The game comes directly from PSN Store, you will be able to go online, get updates, etc.
After the setup process, the game will be available to launch on your own account, just as any other game or app you purchased directly in PSN Store.
Destiny is an action-adventure, shared-world shooter. As a Guardian, you will traverse the planets and stars, fighting for our survival and to keep hope alive. That doesn't mean you have to do it alone. If you wish to, you can play Destiny completely alone (Although content such as raids and strikes require you to play with other players), or you can go in with a fire-team of you and up to two others. Players can seamlessly be matched into your game to help you fight and explore. Public events will also be available to participate in. The game includes multiplayer modes like, Skirmish, Rumble, Salvage, Clash, Combined Arms, Control, and Iron Banner. Destiny is your story; you craft it and wield it. Use it well. Be Brave.