The bore of a labrosone is the characteristic shape of the acoustic tube. It has two main parameters: the taper (conical or cylindrical) and the diameter. The taper affects the timbre of the instrument: generally, a cylindrical bore makes a brighter timbre, and a conical bore makes a mellower timbre. The diameter determines whether the fundamental or the first overtone is the lowest feasible note to play upon the instrument: in a whole-tube instrument, the fundamental can be played with ease, and the diameter is large for the length of tube, but in a half-tube instrument, the diameter is small, and the first overtone only can be reached.
(Half-remembered, half-copied from Wikipedia.)