The antenna was a biological feature of the Andorian species and their Aenar subspecies. Both had a set of two antennae, capable of movement, on the top of their head. The twenty-second century Andorian Shran once demonstrated that antennae were moved by voluntary muscles that could be controlled separately from one another. (ENT: "United")
At least in the case of Andorians, the antenna aided in balance. If one was lost, an Andorian became partially disabled in the short term, although they would start compensating within days. The antennae would eventually grow back, within nine months if left untreated, and in half that time with the use of electrical stimulation and brisk cranial massage. All in all, the loss of an antenna was not considered critical, although it might be considered humiliating. (ENT: "United")
Placement and shape
The placement and shape of Andorian antennae might vary significantly. Most Andorians in the 22nd century pre-Federation Imperial Guard sprouted antennae from their frontal skull bones. This Arrangement was also seen in the Aenar. Ambassador Shras and his delegation sported antennae which sprung further back, off their parietal bones. (TOS: "Journey to Babel") Yet others had longer and thinner antennae. (Star Trek: The Motion Picture; TNG: "Captain's Holiday", "The Offspring")
In 2154, captain Archer cut off one of Thy'lek Shran's antennae during an Ushaan, rendering him defenseless and thus respecting the tradition without killing him. "What good is a Guardsman without two antennae", Shran lamented afterwards. (ENT: "United")
When Lisa Cusak was a Junior officer stationed on Andor she met a person that kept pointing his antennae at her whenever she walked through his office. At first she thought it rude, but she ended up dating him for six years. (DS9: "The Sound of Her Voice")
Some other species also had antenna-like features, for example the Xindi-Insectoid, Species 6339, and the Alfa 177 canine, but antenna were only ever pointed out and discussed by name in reference to Andorians.
The Andorian antennae seen in "Journey to Babel" were sculpted out of clay by makeup artist Fred Phillips using the ends of thread spools for the tips while the main stems were made of a rigid material and attached to the white wigs. (Star Trek: Aliens & Artifacts, p.49)
For more detailed information on the Antenna makeup (and the changes in appearance through the years), see the background section of the article on Andorians.
In the Pocket DS9 novel Avatar, the Andorian Shar keeps picking up signals through his antennae during a visit to Deep Space 9 in 2376. While in Quark's, he is able to focus on one of the signals and detect a pair of shrouded Jem'Hadar soldiers.