of an organism
that once served
a useful purpose
but, as the organism evolved
, stopped serving a useful purpose, yet remains a part of the body
. This can also include organs that appear during development, yet disappear later on.
There are quite a few animals and plants that have such organs. Humans have tails while embryos, and wisdom teeth - not only vestigial, but can cause problems for some people who have a mouth that's too small for them. There are snakes with rudimentary legs. Flightless birds with wings and hollow bones. Some whales have hip bones - but no hip. Crabs have tails under their shells.
There is evidence by looking at some odd "design" of some parts of animals that vestigial organs have a tendency to be "jury-rigged" into serving some other purpose, once they stop being needed for their previous one.