If something is "spindle-shaped" it's tapered at both ends. The term comes from the shape of thread-holding "spindles" used on weaving and sewing machines, and from the earlier practice of spinning wool on a spinning wheel. As the yarn was spun it was wound onto a spindle like this one. A "spindle" can be almost anything that revolves and/or has something rotating on it. Industrial textile machines use spindles that rotate at high speed, and have the same shape at both ends so that orientation on the machine isn't a concern. It happens that this double tapered shape occurs quite commonly in biological structures, as it's admirably adapted to many other applications.