According to the
Jargon File (see
Mongolian hordes technique), the term originally referred to an
orgy! However, once the
military began using a similar phrase to refer to situations ranging from a logistical
SNAFU to a
bloodbath (see
clusterfuck), I can see the changeover described by
sl0throp occuring.
Why "
Mongolian?" If we look at the associated
jargon file definition, then it probably refers to the idea of
Genghis Khan's ancient
Mongol hordes, and their bringing of terror and disorganization. A distant second-place guess would be some relation to the term
mongoloid, which was at one point an acceptable descriptor for a person with
Down's Syndrome (it has since been abandoned, because of its inaccuracy and its unfairness to people of
mongoloid races).