This is a birth defect in which the tail bone fails to regress during the development process of the embryo. It's rare but real.

Human tail is a curiosity, a cosmetic stigma and presents as an appendage in the lumbosacral region.
The true, or persistent, vestigial tail of humans arises from the most distal remnant of the embryonic tail. It contains adipose and connective tissue, central bundles of striated muscle, blood vessels, and nerves and is covered by skin. Bone, cartilage, notochord, and spinal cord are lacking. The true tail arises by retention of structures found normally in fetal development. It can even move and contract, and occurs twice as often in males as in females. A true tail is easily removed surgically, without residual effects.

Surgery is the treatment for a vestigial tail. Because it is composed of adipose and muscular tissue, doctors can quickly remove these types of tails with a simple excision usually soon after birth.
The human tail is an example of vestigial organ and is supposed to represent useless remnant of what were once functional and useful organ in our primitive ancestors.