The Quincy were once an organization of humans possessing spiritual who killed Hollows. They were intrinsically different from the Shinigami in this regard; whereas Shinigami sent Hollows on to a peaceful afterlife, the Quincy simply destroyed them. The Quincy didn’t see why Hollows, who killed humans and ate their souls, should be allowed to peacefully go on to the next world. Many had loved ones and friends who were killed by Hollows. Thus, they justified their stance.
The Quincy posed a serious problem for the Shinigami. To keep the world in balance, the number of souls in the Soul Society must equal the number of living people here. A Shinigami’s job is to regulate the number of souls who enter the Soul Society and the number of souls who leave and are reincarnated. Hollows are included among the entering souls. By destroying the Hollows the Quincy upset the balance, as outgoing souls do not return. If the balance is aggravated enough, the two worlds will spill into one another, ensuring the destruction of both. The Shinigami originally appealed to the Quincy, asking them leave the handling of Hollows to them, but the Quincy refused. As the Quincy increased in number and spread across the world, the Shinigami felt that they had only one option left: to destroy the Quincy. So, they did. Most agree, even Uryuu, that the Shinigami were right to sacrifice the few to save the majority.
However, the Shinigami are were not completely just in their effort. Kurotsuchuchi Mayuri, one of the 13 Shinigami captains and president of the Research Institute of Technology, took a special interest in studying the Quincy. By that time, though, most of the Quincy had been wiped out; there weren’t many test subjects left. So, Mayuri bribed the Shinigami protecting the Quincy from Hollows to show up too late to save them. After they died, their souls were brought to Mayuri, who tortured 2,261 subjects to (a second) death. “I’ve finished studying the Quincy”, he tells Uryuu in the Soul Society, “Opened skulls alive, forced one to burn his own son to death, chopped up bodies...grinded bodies...studied them until they were rendered to piles of lifeless limbs” (Chapter 123). The end in view may have been noble, but the Shinigami’s methods of dealing with the Quincy were unnecessarily brutal and unjustly cruel.
This was about 200 years ago. When Uryuu first revealed that he was a Quincy, Rukia, who comes from a noble Shinigami household, had never even heard of them. Following Souken’s death, Uryuu and Ryuuken are the only two Quincy left.