Apparently, according to the Galaxy class deck blueprints, as shown on Memory Alpha, Deck 36 houses a "Droid Maintenance" room. A series of convention notes from Rick Sternbach's panel at AnimeCon '91 also mentions it:
Going into the bowels of the ship, you will eventually find a door marked DROID MAINTENANCE...
What exactly goes on in Droid Maintenance, and has it ever appeared on-screen or in written materials?
The only "droid" we regularly see is Data.
Ideally I'd like the purpose explained both in and out of universe, or at least an in universe mention. Even just the door tag appearing briefly would count. I would accept any published sources, including novels or comics if no canon references exist. Out of universe, my guess is it was just a comical reference to Star Wars. (the production crew filled the ship with various references) Some kind of statement confirming that would be nice.