According to Seed Savers Exchange, the rat-tailed radish is native to South Asia and used not for the root, but for the bean pods the bush produces. It is a rather large bush covered profusely with lovely lavender flowers that serve as a warning as to just how many beans it will soon be producing.
The root is large and unappetizing, to say the least. Radishes are part of the Mustard family, and the name comes from the Latin word radix, meaning "root". The common radishes that most of us are familiar with may have originated in China, but eventually made their way to Egypt, Greece, and Italy. They were introduced to the New World around 1500, and were one of the crops grown by English colonists in America. The rat-tailed radishes (Raphanus sativus 'caudatus') may have originated in India sometime in the 1800's.
The bead pods grow vertically on the branches of the bush. The catalogue says to harvest them before they are fully grown, which is at 4-6" in length, so they are ready for harvest now. I planted the seeds directly outside on May 23rd, so they have taken about eight weeks to be ready to harvest. I bought these seeds because I like to grow unusual vegetables, and I have not been disappointed. Apparently, the are supposed to be eaten raw, though they look rather sharp to me, with the ends growing up all straight and pointy.