From the German for "Basic shape", or if you want to be a little more literal, "ground gestalt." Used in music theory to refer to the fundamental concept underlying a musical work, the features of which influence and determine specific ideas within the work itself. Or to put it in much more simple terms, Grundgestalt is a feeling or spirit that suffuses a piece of music. (Some will define it simply as the "basic musical idea". But that's a little bit too simple.)
The idea comes from the writings of Arnold Schoenberg; although he invented the term, he never gives a strict definition. A lot of people have spent a lot of time arguing what exactly Grundgestalt means, where it resides, and how to quantify it. No one has come up with a definitive answer yet, but it's fueled a number of academic theses.