Though Sir Simon is a prominent figure in the story, the reader doesn't really ever know that much about him. We know some details from characters like Mrs. Umney, but we aren't sure if what she says about the ghost is absolute fact or not. Throughout the story, readers get to see what the ghost is attempting to do to the Otis family and how the Otis family antagonizes Sir Simon right back; however, those things don't give readers any insight into what his life was like before he became a ghost.
That changes in section five of the story. Section five begins with Virginia stumbling across Sir Simon pouting by the window.
To her immense surprise, however, it was the Canterville Ghost himself! He was sitting by the window, watching the ruined gold of the yellowing trees fly through the air, and the red leaves dancing madly down the long avenue. His head was leaning on his hand, and his whole attitude was one of extreme depression.
Readers are told that he looked so pathetic that Virginia couldn't help but begin a conversation with him. Early in the conversation, Virginia mentions that she knows that Sir Simon killed his wife when he was alive. Sir Simon completely embraces the fact that he killed his wife.
"Mrs. Umney told us, the first day we arrived here, that you had killed your wife."
"Well, I quite admit it," said the Ghost, petulantly, "but it was a purely family matter, and concerned no one else."
Sir Simon essentially feels that his actions were completely justified and normal. He provides Virginia with further "evidence" as to why his wife deserved to be killed. He says that she was "plain" looking, not good at laundry, and not a good cook.
"My wife was very plain, never had my ruffs properly starched, and knew nothing about cookery."
The final detail that Sir Simon reveals about his past life is how he died. His wife's brothers starved him to death.
From their brief conversation, it seems that Sir Simon's life is vaguely similar to his life as a ghost. He is used to being the person that is running the show. He enjoys exerting his power and opinion over other people, and he doesn't care who he hurts or offends while doing it. That's why he sees no problem with killing his wife for minor offenses, and it's why he believes that he is justified in haunting the house all these years.
"It is absurd asking me to behave myself," he answered, looking round in astonishment at the pretty little girl who had ventured to address him, "quite absurd."