This is an old posting I just rec'd.. but in case you had few answers,
check in older herbals ,  books on housewifery, cooking.. I know I encountered
the term in Elizabethan works,  Mrs. Raffalds Cookery..most large households
seem to have had a small room, similar to a pantry, with a dry sink, wet
sink, heat source, tools for pounding, infusing, for various household
needs, including  remedies, potpourris, salves, furniture polish, and in
earlier times, the expensive spices would also be kept there under lock
and key.   The term might be based on distilling that took place there,
or just  that drying herbsneeded to be kept somewhat dust -free.  Later
recommendations include  enclosing them loosely in a cloth or paper bag
to hang, in order to keep off smoke, dust and insects.
You might also try to get a copy of Sir Kenelm Digbies Closet Open'd,
where I think you'll find description of the ideal setup.