"Breeders" was a pejorative name applied to a race of humans on the planet Euronda by their enemies, the Eurondans. It is known that they at least had racial phenotypes that correspond to Caucasians and African-Americans on Earth, but it was stated that they are made of "all shapes and sizes, and all colors," so it can be supposed that their population is as diverse as modern Earth's North America.
They were alleged to have bred freely with various members of their population with no regard for what the Eurondans considered "genetic purity". For this reason they posed a threat to the Eurondans, who possessed a Hitleresque ideology of a genetically pure race. Led by Alar's father, the Eurondans conceived of a plot to exterminate their enemy by filling the atmosphere with poisonous gas while they hid in an underground facility. But the Breeders discovered and thwarted their plan, and a war between the two peoples began.
Breeders possess the technology to create unmanned recon drones, as well as advanced, manned bombers. At the time of SG-1's arrival, Breeders were winning the war and controlled most of the planet.
When they learned of the Eurondan's ideology and attempted genocide, SG-1 aided the Breeders in assaulting the Eurondan bunker. With the Eurondan hideout fatally damaged, it is likely that the Breeders had no problem winning the decades-long war following SG-1's departure and Alar's apparent death. (SG1: "The Other Side")