Here is the Wikipedia article on Kosminski. According to the article:
An 1894 memorandum written by Sir Melville Macnaghten, the Assistant Chief Constable of the London Metropolitan Police Service, names one of the suspects as a Polish Jew called "Kosminski" (without a forename). Macnaghten's memo was discovered in the private papers of his daughter, Lady Aberconway, by television journalist Dan Farson in 1959, and an abridged version from the archives of the Metropolitan Police Service was released to the public in the 1970s. Macnaghten stated that there were strong reasons for suspecting "Kosminski" because he "had a great hatred of women ... with strong homicidal tendencies".
In 1910, Assistant Commissioner Sir Robert Anderson claimed in his memoirs The Lighter Side of My Official Life that the Ripper was a "low-class Polish Jew". Chief Inspector Donald Swanson, who led the Ripper investigation, named the man as "Kosminski" in notes handwritten in the margin of his presentation copy of Anderson's memoirs. He added that "Kosminski" had been watched at his brother's home in Whitechapel by the police, that he was taken with his hands tied behind his back to the workhouse and then to Colney Hatch Asylum, and that he died shortly after. The copy of Anderson's memoirs containing the handwritten notes by Swanson was donated by his descendents to Scotland Yard's Crime Museum in 2006.For those wanted a more detailed account of Kosminski's life and clues that point to him as the killer, see this article at Casebook. And an article from Crime Library has some more information on why the police identified him as a suspect.