A drop spindle is a very old tool for turning unspun fibre (roving) into thread or yarn. It's a dowel about 8-10 inches (20-25cm) long with a disk, or in some cases one or two crossbars, mounted near one end. The whorl (or crossbar) stabilises the spindle so it spins longer and more evenly. Typically, it will also have a hook or a notch in one end of the dowel to hold the yarn in place.
There is archaeological evidence for string - fibres from some plant or animal source drawn out more or less parallel to each other and twisted together - dating as far back as the Palaeolithic age. Spindle whorls appear in the archaeological record around 5,000BC, and drop spindles were the primary tool for spinning until the invention of the spinning wheel sometime in the 13th c.
Using a drop spindle is much more easily demonstrated than explained; I strongly recommend finding a teacher, or failing that, looking up videos on that great gift to craft instruction, YouTube. The general principle is something like this:
The spinning spindle imparts extra twist to the existing yarn, which is pinched between the fingers right at the transition point between the unspun roving and the twisted yarn. By pinching the roving an inch or two further up with the other hand, and releasing the original grip, the twist travels up into the unspun fibre and turns it into yarn. Repeat until the yarn is so long that the spindle hits the floor, wind it onto the shaft of the spindle, and continue until you run out of roving.
Ideally, the resulting yarn will be even, and twisted tightly enough to hold together, but not so tightly that it kinks on its own. This takes practice.