In a nutshell, story of this OVA involves a girl named Mato Kuroi going to school meeting another girl called Yomi Takanashi, eventually attempting to befriend her. She suceeds and two hang out together until Mato starts hanging out with a guy/girl(?) named Yuu. Yomi becomes saddened because Mato stops hanging out with her because she is hanging out with Yuu instead, and over time Yomi mysteriously disappears. When Mato realizes she is gone, she tries to search for Yomi and eventually discovers where she is.. Saying anymore than that would give away spoilers, so watch it if you are really curious as to what else happened.
Though I am very new to Vocaloid/Black Rock Shooter or anything relating to those two, I did enjoy this anime a fair bit. Some parts of it were a little confusing at first however due to the fact that it seems as though the anime randomly switched between the real world, and wherever it is Black Rock Shooter's world is. In the real world, there would be normal events like Mato going through school life and having fun with friends and whatnot. In Black Rock Shooter's world, there would be fighting going on between another person called Dead Master and herself. Not much is really explained as to why these two are fighting though, so I guess you had to have already been a fan of the series to know that.
Putting the fighting aside, if you happened to watch some of the trailers that were displayed all over the internet, you might've noticed that Black Gold Saw and Insane Black Rock Shooter were featured in those, both working together against Dead Master. They're completely absent from this "special" for whatever reason. They probably went where the character development went. In a deep, dark abyss of doom in which you can never return from. Hey, at least the action was good when it actually showed any fighting.
I think that it might have been better for the developers to stretch this anime out into at least three OVAs or maybe just extend it into a full twelve or more episode anime so that things such as character development and story could be more detailed and less rushed, as there clearly was not enough of either of those in this OVA. If you plan on watching this, I would suggest that you already be a big fan of Vocaloid and/or Black Rock Shooter and understand that will be rushed, otherwise you may find yourself not liking this too much.