In the Star Trek universe, the Breen are a reclusive alien race from a planet of the same name.
Though mentioned in passing numerous times, not much detail was given about them, and what was revealed simply expands the mystery. Breen always wear full-body refrigeration suits obscuring their features. Allegedly, this is because they're native to an ice planet, but in DS9 episode The Changing Face of Evil, the Vorta Weyoun reveals that the Breen homeworld is actually quite temperate.
Though seemingly very isolationist, the Breen Confederacy is militarily powerful. An attempted invasion of Breen by the Klingon Second Empire failed miserably, and upon joining the Dominion, the Breen proved a very powerful adversary, their weapons handily disabling Federation and Romulan ships (and all Klingon Birds of Prey save one) (DS9: The Changing Face of Evil). As an aside, Klingons, Romulans, and Breen are the three races that use Type 3 Disrupters, and their ships have cloaking technology.
While alien speech in Star Trek is usually heard by viewers in English (with the occasional bit in Klingon or another human-pronounceable language) thanks to universal translations, the Breen have a speech that sounds decidedly non-human, consisting of garbled electronic sounds.
As mentioned, the Breen supposedly need refrigeration suits, and yet their home planet is (according to Weyoun) temperate. A mystery indeed. The Breen have been known to provide the Maquis with cold-storage units (DS9: For the Uniform) and non-canon sources claim to have traded Warp technology to the Ferengi in exchange for the two poles of Ferenginar, several comets, and a frozen moon. Additionally, they allegedly eat an algae paste that is the only thing capable of growing in their frigid environment.
The Breen come up numerous times throughout TNG, DS9, Voyager, and Enterprise, but they are by far most prevalent in the last season of Deep Space 9.
Episodes that mention the Breen in passing include
TNG: The Loss, TNG: Hero Worship, TNG: Interface, DS9: Shattered Mirror, DS9: Business as Usual, DS9: For the Uniform, DS9: To the Death, VOY: Elogium, VOY: Scorpion.