The Skrreea lived in a matriarchal society, as Skrreean males were considered far too emotional to be leaders and were constantly fighting among themselves. It was not unusual for Skrreean females to have multiple spouses.
The Skrreean also had an unusual skin condition which caused them to leave flakes of skin behind. This caused those who were unused to it to treat Skrreea with disdain and believe that they were "dirty".
The Skrreean spoken language had a unique syntax and grammatical structure which caused the universal translator to struggle with it initially before it could establish a translation matrix. (DS9: "Sanctuary")
By 2370, the T-Rogorans were themselves conquered by the Dominion. The Skrreea took this opportunity to flee their homeworld in whatever ships they had, in search for the Eye of the Universe of Skrreean legend. One ship, carrying Haneek and her family, discovered the Bajoran wormhole and identified it as the Eye. Arriving at Deep Space 9, Haneek studied Bajoran history, and assumed that Bajor was Kentanna, a planet named in Skrreean legend as a "planet of sorrow" where the Skrreean people were destined to settle. Some three million Skrreean refugees subsequently arrived at Deep Space 9 in search of aid.
With no established government, the Skrreea chose Haneek as their leader. Haneek petitioned the Bajoran Provisional Government to allow her people to settle on Bajor. They proposed to use their agricultural technology to reclaim land that was poisoned by the Cardassians and thus they would be able to support themselves, without relying on the Bajorans. The Bajorans still refused, insisting that they were struggling to provide for their own people's needs and could not take in three million refugees; if something were to go wrong with the Skrreean's plan, the Bajorans would feel obligated to help them for humanitarian reasons.
Haneek's teenage son, Tumak, was angered by this decision and attempted to land one of the Skrreean ships on Bajor. Unfortunately, Tumak was unaware that the Skrreean ship had suffered a high-energy radiation leak. During a short battle with the Bajoran Militia, phaser fire ignited the radiation leak and destroyed the Skrreean ship, killing Tumak.
The spelling of the Skrreean race comes from the script for "Sanctuary" which also gives the pronunciation as "SKREE-uh". Of their appearance, it goes on to describe, "...their garb is scruffy, their dark skin an off-putting mass of lumps and eczema-like scales." 
In designing the appearance of the Skrreea, the producers specifically wanted none of the standard makeup appliances to be used at all. Instead, they asked the makeup department to create a skin texture that made them stand out. Makeup Designer Michael Westmore suspended tiny clay balls into a layer of latex and applied that to the surface of the actors' faces. When it dried, the coating looked like a layer of skin with hundreds of bumps spread throughout. Although the first test subject was regarded as looking like a Human with a terrible skin disease, the entire group of actors together were deeped to look like a race. (Star Trek: Aliens & Artifacts, pp.152-153; Michael Westmore's Aliens: Season Two, DS9 Season 2 DVD special features)
In the Star Trek: Deep Space Nine - Mission Gamma novel Cathedral, the character Vedek Solis Tendren recalls the Skrreean problem when settling the Europani on Bajor. Tendren wishes that the Skrreea had been allowed to settle on the planet and farm the land as by 2376, the northwest peninsula is still underdeveloped.
The Skrreea are mentioned by Doctor Meron Byxthar in the Pocket TNG novel Losing the Peace. A sociological expert, Byxthar once observed life on the Skrreean communes on Draylon II as part of her work.