What is the history behind the bloodstain, and why did the ghost take great efforts to repair it?

In Chapter One of "The Canterville Ghost," Mrs Umney informs the Otis family of the history of the famous bloodstain. It is the blood of Lady Eleanore de Canterville, who was murdered on "that very spot" by her husband, Sir Simon, in 1575. Later, in Chapter Five, the reader leans that Sir Simon murdered Eleanore because she was "very plain" and poor at housekeeping. She never starched his ruffs properly, for example, nor did she properly serve a buck that he had shot. 

Because of its personal history, Sir Simon, the ghost, goes to great pains to preserve his wife's bloodstain in the library. After Washington Otis removes it with Pinkerton's Stain Remover, the family finds that the bloodstain has reappeared every morning. Virginia Otis later learns (in Chapter Five) that the ghost stole her paints so that he could "furbish up" the stain each night. This also explains why the stain appears in different colours, including vermilion and emerald green. 

The bloodstain, then, is a physical reminder of Sir Simon's past crimes and of the house's murderous history. It also acts as a barrier to Sir Simon's eternal rest: the stain cannot be truly removed until the ghost repents of his sins and has left Canterville Chase.