Their planet was endangered by severe cooling of the planet's molten core. The USS Enterprise-D stopped the problem for several hundred years.
The Atreans had a saying, "A child born from parents who love each other will have nothing but goodness in his heart." (TNG: "Inheritance")
In the first draft script of "Inheritance", this species was called the "B'Cray". Also, a scene description in the same document stated, "The B'Cray are a humanoid species, only slightly different from us."