GIST is an odd little word that I have heard used my entire life and never known the origin. People say "What was the gist of it?" meaning what was the essence or essential part of a matter In law, it has a more specific meaning, the real point of an action, as in "damages are the gist of the lawsuit."
The word appeared in the early 18th century and comes from Old French, gesir "to lie" and earlier from Latin jacere. The legal connection seems important as there was (is?) an old legal phrase cest action gist that was used in France and England meaning "this action lies." That phrase denoted that there were sufficient grounds to proceed. "Lie" here means more like the way we use it today when we say "The difficulty lies in getting sufficient funds."
I came to all of this when I was writing about memory. There is a kind of false memory that is sometimes called "gist memory." Gist traces are fuzzy representations of a past event when we have the general idea but not the specifics of the event clear. Verbatim traces are detailed representations of a past event. It seems that although people are capable of processing both verbatim and gist information, they oddly prefer to reason with gist traces rather than verbatim.
The older I get, the more I seem to be relying on gist memories if I remember something at all!