To get a great deal of information about Sir Arthur Conan Doyle’s “The Adventure of the Spotted Band,” follow the links to the right of this question. This can help you with any questions you may have about the story. The quick answer to your question is that the villain is Dr. Grimesby Roylott, who is the stepfather of Helen Stoner, the young woman who comes to Sherlock Holmes for help.
In this story, Roylott married Helen’s mother some years before. Helen had had an older sister but that sister died in mysterious circumstances not long before she was going to be married. Now Helen is engaged and there are mysterious things happening around the estate where she lives with her stepfather. Her mother died eight years before the events of this story.
At the end of the story, we find that Roylott is the villain. He wanted to kill his stepchildren because, if he did so, he would not lose any of the money that his wife had bequeathed to them. Thus, the motive for his attempted murder of Helen (and, we presume, of his actual murder of her sister) was Roylott’s desire for money.