from yoshida on twitter
it's automatic, not install but caching data
Basically, instead of installing data from the disc to the HDD, the PS4 will use a caching mechanism to store files frequently used for the game on the HDD. So, instead of having a 15 minute install when you first put the disc in the game, it'll "install" the files as you play, putting the files it frequently needs on the HDD. Since it's a cache, it will be dynamic and delete files not used as often when the cache needs additional space.
So, you put in a game, and as it loads, it will load the main character, enemies and level 1 assets and those go onto the HDD. You finish the first level and it loads level 2, and puts level 2 into the cache. You go to level 3, but your cache is now full (hypothetically, probably from other game caches). The cache sees you are still frequently using the player and enemies assets, but haven't used the level 1 assets in some time, and removes the files for level 1 from the cache. Your friend comes over and starts a new game. The cache wants to re-load level 1, but, again, not enough space, and removes level 2 from the cache (the assets that have not been used for the longest).