A Fach is a compartment in a larger container or piece of furniture. In a more figurative sense, the word denotes a specific area of expertise, often acquired through a course of study devoted to this particular field (civil engineering is an example). In the performing arts, Fach denotes the vocal range and related specialization of a singer (for example, lyrical soprano or Heldentenor) or the type of role an actor is particularly suited for (for example, action hero or ingénue).
An Idiot in German is the same as an idiot in English. In combination with Fach, we get a Fachidiot, a person totally focused on or only interested in his special area of expertise while remaining clueless with regard to anything outside that area. Fachidiotin is the female form, but I've heard the masculine form applied to persons of either sex.
Addendum (Dec. 5, 2015). Here's an article that explicitly refers to the German term in connection with one of the hopefuls for the Republican presidential nomination (Ben Carson): The GOP and the Rise of Anti-Knowledge.
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