Blizzard adopted this model on World of Warcraft and Diablo 3 a while back. It works in co-junction with the launcher for big patches and digital downloads.
The system allows you start playing the game without downloading it entirely. If you reach a point where missing data is required, it will download it then. (It will also continue to download the rest of the data in the background, as well).
I saw the "streaming data" message once after I had already downloaded everything, checking my bandwidth monitors confirmed it was not downloading from the internet.
Therefore, we can conclude that when the "streaming data" message appears the game first searches for the required data locally, if it finds it is available, it then loads it into memory, if it is not, then it can fall back to downloading from the internet.