Tribbles are small, soft, gentle animals of the Star Trek universe whose cute appearance and soothing purring endears them to every sentient race which encounters them - with one notable exception. They are essentially small bundles of fur with no visible external features. Their only two purposes in life appear to be to eat, and to reproduce; they perform both of these functions extremely well.
Klingons are unique among Star Trek's races in their extreme hatred of these cute little creatures. This is because tribbles emit a loud shrieking noise in their presence.
Tribbles were originally encountered in the original Star Trek television series, in an episode titled "The Trouble with Tribbles." Captain Kirk and his crew encounter the Tribbles on a space station while arranging to transport some grain to a colony. The "trouble" with Tribbles is that they reproduce far too quickly - in the words of Dr McCoy, "They are born pregnant" - and threaten to clog up essential ship systems.
In Deep Space Nine episode "Trials and Tribble-ations" the crew of the USS Defiant encounter the Tribbles once more. Since Worf reveals that the creatures were actually hunted down and exterminated by his people, this can only be achieved by time travel. Fortunately, or perhaps unfortunately depending on one's perspective, a number of tribbles were brought back to Deep Space 9 from the past and the species is reestablished. It is not known if this was deliberate or not.