(covers information from several alternate timelines)
Breen was an inhabited planet in the Breen system. This system was located in the Alpha Quadrant. As the homeworld of the Breen, a warp-capable humanoid species, it was the capital of the Breen Confederacy and, in 2375, was allied with the Dominion. Little was known about the planet Breen, but it was widely believed to be a frozen wasteland. (DS9: "Indiscretion", "For the Uniform", "What You Leave Behind")
During the Klingon Second Empire, Chancellor Mow'ga ordered an entire fleet of Klingon warships to invade and conquer the Breen homeworld. The fleet never returned and was never heard from again. (DS9: "'Til Death Do Us Part")
Upon learning that Odo was in love with Kira Nerys, Quark was surprised that Odo was capable of such feelings, as he had always thought the changeling was "as cold as a Breen winter." (DS9: "Crossfire")
In 2372, Gul Dukat, knowing how Cardassians hate cold, dreamed about demoting his rival Gul Marratt and assigning him to the Cardassian embassy on Breen after Dukat regained his own former posting to the Detapa Council. (DS9: "Return to Grace")
In the first draft script of "One Little Ship", Ixtana'Rax mentioned this planet upon threatening a pair of Jem'Hadar guards who, under Kudak'Etan's supervision, had brutalized Captain Benjamin Sisko. Ixtana'Rax told them, "If this man is struck again, by anyone, you will both be reduced six ranks and assigned to escort the wives of Cardassian diplomats on inspection tours of the Breen homeworld." Indicating the seriousness of this threat, the script's stage directions then likened this to "being ordered to guard a weather observation station at Point Barrow, Alaska."
At a time when the only character to have referred to Breen as "a frozen wasteland" was Dukat (in the episode "Indiscretion"), Star Trek: Deep Space Nine - The Official Poster Magazine (No. 4) reckoned that, considering the metabolism of Cardassians, the fact Dukat had referred to the planet that way might mean it was actually "just about right for Humans."
According to Star Trek: Star Charts (p. 36), Breen was a P-class planet (the class was conjectural). The dominant species was the humanoid Breen. Information was not available on when the Breen became warp-capable, the world's population, or even the name of the capital.