You are right. Eastern Orthodox still practice this in a way, though it is not called the "Black Fast". As I am an Orthodox Christian I can tell you that we do fast every Wednesday and Friday, though not as strictly as the Black Fast. It's more like eat vegan, basically the same as you listed, but we get 3 meals at the regular times, though some people may do it more strictly including monastics. Also don't eat as much.
Then we also have as we call it the Great Fast, or Great Lent, that starts 40 days before Holy Week. Basically we eat the same as on Wednesdays and Fridays, also trying more then normal to abstain from sin (that's the whole goal right?). Then during Holy Week the rules change and it is a little more strict, namely maybe 1 meal a day, on special days (Holy Thursday: the crucifixion) eating nothing at all. Check out [wikipedia][1] for more info.
We also have fasts before the Dormition (two weeks long called the Dormition Fast), a fast called the Apostles Fast, and A fast before Christmas, called Advent. According to Wikipedia, Advent starts on the fourth Sunday before December 25, which is the Sunday between November 27 and December 3. According to my Orthodox Calendar, this year it will start on November 15.
Also I forgot to mention, that on the first week of Great Lent we have a strict fast from Monday to Wednesday, thats a strict fast meaning no food at all. For the weak, (Children, Elderly, Pregnant) there are exceptions.
Of course thats not all the fasts that we do. Check [this link][2] for more info.
OK, just checked back at your question and saw that you asked why it is done. Um, kind of for the whole going to heaven thing that we're doing as Christians. Depriving the body of food is supposed to help with repentance and to humble the body to the Spirits will.
Hope that answers your question! If not I can say even more. [1]: http://en.wikipedia.org/wiki/Great_Lent [2]: http://www.abbamoses.com/fasting.html