As I understand it from this article, not the complete data of the blu-ray disc has to be installed at once, when you play a game:
http://kotaku.com/how-mandatory-game-installations-will-work-on-ps4-1462283797
The data you load from the blu-ray will be cached on the hard drive, so the next time they can be loaded much faster. You don't play multiplayer? The multiplayer maps don't have to be cached on the HDD. You only play the first levels of a game? The unplayed levels won't be cached on the HDD (perhaps the next segment will be preloaded). You don't watch "Making-ofs" or other Extras? They won't be cached, perhaps movie files won't even be cached IF you watch them.
If you need more free space on the HDD, you delete the caches of the games you don't want to play in the near future.
With the caching on the HDD, developers can depend on sequential transfer speed of at least 80 - 100 MB/s... the maximal bandwith of a 6x BD drive is 27 MB/s... a huge difference, especially for open world scenarios.
The iFixit teardown revealed a Hitachi Travelstar Z5K500:
http://www.storagereview.com/hitachi_travelstar_z5k500_review_hts545050a7e380
Newer 2.5''-HDDs with higher capacities will be even faster, the SATA2-limit is 3 Gbit/s... theoretically 384 MB/s, realistically around 250 GB/s.
"Cerny said his team had heard too many complaints from current-gen developers about having to wait to load in new levels of games. Putting the data on the readily-accessible hard drive alleviates that."
