From the archives:

Cauda equina comes from the Latin cauda (tail) and equina (horse). The "horse's tail" is an appropriately named collection of dorsal and ventral spinal nerve roots that hang off the spinal cord.

The the term was coined in 1600 by the French anatomist Andrea Laurens (also known by his latinized name, Andreas Laurentius).

Andrea Laurens's original drawing of the cauda equina, with this accompanying description (translated from the Latin): "Spinal cord displayed after immersion in water with all of the nerves exiting in a hair-like configuration suggesting a horse's tail..." http://radiology.rsnajnls.org/cgi/reprint/169/2/320.pdf

The rabbinical writers of the Talmud in the second century A.D. were the first to describe the structure. The Talmud was not an anatomy text of course, but accurate anatomical descriptions were required so that rabbis, when examining sacrificed animals, could determine whether the meat was either kosher or trefe, i.e. unsuitable, according to Jewish law.

Interestingly, the ancient rabbis were more accurate in their accounts than the two greatest anatomists of the enlightenment, Andreas Vesalius (the first "modern" anatomist) and Thomas Willis (the father of neuroanatomy). Both failed to recognize the cauda equina's existence, over a dozen centuries after the Talmudic accounts, even while providing detailed drawings of the spinal cord and its nerves. Vesalius was active a couple of generations before Andrea Laurens. Willis, from England, worked a couple of generations after Laurens, apparently unaware of the Frenchman's accomplishments.

Other anatomical structures with cauda in their names include the caudate lobe of the liver (meaning "towards the tail " or in this context, inferior) and the caudate nucleus of the cerebrum, a mass of gray matter with a long tail. The coda, or the "tail end" of a musical composition, is also derived from cauda.