Each person gets to establish one PS4 as their primary system. Games downloaded by you on that system can be played by others, even without logging into your account. The same thing holds true with a Playstation Plus membership, where others can play online in titles that require it.
When it comes to other systems that aren't designated as the primary one, only your account can download and start up the games that you have purchased. Note that there is no limit to the number of systems you can download a purchased game to. The same holds true with a Playstation Plus membership, as only that account will enjoy its benefits.
The above only applies to PSN titles, as retail discs are not tied to a particular account. This means that you can rent and share retail titles with friends, without having to connect to the internet or pay any fees for used games.
