In the Star Trek universe, the Trill are a humanoid alien species and the symbionts that sometimes live inside them, both from a planet of the same name.
Trill differ in appearance from humans only in the spots that along their sides from the top of the head to the feet. In their initial appearance in The Next Generation episode The Host, the Trill Odan and Kareel have triangular forehead ridge and no spots. The symbionts are rarely seen, as they reside inside the torso of the host Trill. They would be best described as space slugs, in appearance.
The Trill government perpetuates a myth that most Trill cannot be joined with a symbiont. In fact, most can, but are not considered worthy, and there aren't enough to go around. Before joining, a host Trill usually goes through an intense screening process.
Notable Trill include the Dax symbiont (ten hosts, including Curzon Dax, Jadzia Dax, and Ezri Dax), Odan, Kareel.
Trill appeared in nearly every episode of Star Trek: Deep Space Nine, thanks to the presence of Jadzia Dax and later Ezri Dax.
It's unclear whether the Trill are part of the United Federation of Planets, though several Dax hosts were part of Starfleet.
Sources
http://memory-alpha.org/en/wiki/Trill
http://en.wikipedia.org/wiki/Trill_%28Star_Trek%29