I have been thinking of what type of organ in the human body would fit into this definition.
One of the things I have read about is that there are some people that
Have a human tail.
Has anyone heard of this and what is it officially called ?

The apendix in humans is a vestigal organ. Vestigal organs/structures are parts of the body that have lost function over a long time like during evolution. There are different types of tails in humans. You can read about it here:Tail - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Vestigial_tail#Human_tails).