Amusingly, there is an "anime collaboration cafe" in Tokyo called SHIROBACO (no direct relation to the anime Shirobako). They have a page explaining the origin of their name:
"SHIROBACO" = "white box"
In the anime industry, this refers to a video recording that is distributed to members of the production staff prior to airing. Though technology has advanced and it has become easier to receive video in digital formats, the video is still referred to as a "white box", just as it was when VHS was in use.
Here is an image of one such white box that I found on some dude's blog:
Sites on the internet are saying that Shirobako had a scene early on where optical discs (which would count as shirobako these days) were being distributed to the people at Musashino Animation. I assume they're right; I don't remember there being a scene like that off the top of my head, but that's probably because I was distracted by Miyamori being cute.
At the end of episode 12, once they have sent the last episode of Exodus to the station, NabeP brings a shirobako (in this case, a white optical disc) of the last episode to the show-completion party.