Why would character be one of the most important elements of the story?

Character in "Lamb to the Slaughter" is important because it helps to create the shock that the reader feels by the end of the story.  

When the reader is introduced to Mary Maloney, she is portrayed as a stereotypical doting housewife.  She is quietly sitting at home counting the minutes until her husband comes home.  

Now and again she would glance up at the clock, but without anxiety, merely to please herself with the thought that each minute gone by made it nearer the time when he would come.

When he finally does come home, she rushes to the door in greeting and then flutters about the room getting him a drink and making sure that he comfortably relaxes in his chair.  Mary doesn't seem to have any other capabilities or desires than making sure that her husband has every need provided for.  

But by the end of the story, the reader has seen a completely different Mary Maloney.  Not only did she kill her husband with one swing, but she calmly went about setting up an alibi for the crime, and she was able to get rid of the murder weapon forever.  

It was extraordinary, now, how clear her mind became all of a sudden. She began thinking very fast. As the wife of a detective, she knew quite well what the penalty would be. That was fine. It made no difference to her.

The shift in character is drastic and jarring.  It in no way jives with the Mary Maloney that was introduced to readers in the opening paragraphs.  Character is key to understanding this story, because Mary's character change is more interesting and central to the story than the actual events of the story.