In the Jack the Ripper story, Jack the Ripper was a very infamous figure. He preyed on women in a poor area of London. There have been many suspects proposed over time, from local butchers to members of the upper class trying to cover up some sordid secrets. But no one has been definitively proven to be him.
Jack the Ripper was indeed a real phenomenon. Although the identity of the perpetrator was never conclusively determined, the series of brutal murders that took place at that time are well-documented and considered a factual part of history.
Jack the Ripper is based on real events. However, some details and theories about the case might be speculative or fictionalized over time. But the core of the story is rooted in actual crimes.