means A small enclosed cage or pen for keeping rabbits or other small animals, or a piece of furniture with open shelves set atop a low cabinet.

from From Middle English 'hucche,' borrowed from Old French 'huche' meaning a chest or storage bin, which traces back to Medieval Latin 'hutica,' a coffer or box — origin beyond that is murky. The thread running through every sense is 'a box to keep things in': first a chest for grain or bread, later the furniture with shelves, and finally the boxy little dwelling we hand to rabbits.