A walnut was an edible seed of any tree of the genus Juglans.
Walnuts were known for their small size, and as such were used as comparisons to other small objects. In 2154, Jonathan Archer goaded Dolim by telling him that Earth dinosaurs had died out because of their small, walnut-sized brains, and insinuated that Xindi-Reptilians were equally afflicted. (ENT: "Azati Prime")
In 2268, James Kirk told Montgomery Scott that the Arretans had the knowledge to teach mankind how to build starships the size of the USS Enterprise with engines the size of walnuts. Scott believed it to be impossible, but added that there wouldn't be anything wrong with looking at the diagrams. (TOS: "Return to Tomorrow")