An official PlayStation 4 FAQ released on PlayStation’s website details how the PS4’s digital game sharing among friends will work.
According to the PS4 FAQ, any games purchased can be played by anyone signed in on a single PS4 designated as the "primary system." Meanwhile, you can attach your PSN account and download games to any other PS4, but on a system that’s not your primary system, you’ll have to be connected to the internet and signed in for any of your content to work. On the primary system, however, offline play of your content will be allowed for any user.
Sony explains the matter as follows: "Games you purchase can be downloaded and played on any PS4 system if you sign in to PSN. There is no limit on the number of systems you can use. Only you can start games that you download."
Registering a console as your primary system is required to enable PlayStation App functionality, PS Vita Remote Play, PlayStation Plus, and a number of other features. As for used games and physical copies, they can be used and shared freely and among friends with no restrictions, as Sony declared at E3 2013.
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