What does Aunt Alexandra mean when she says "somebody just walked over my grave" in To Kill a Mockingbird? There are two reasons: one is related to plot, and one is related to the theme.
Before answering this question, let's first consider the meaning of the expression "somebody just walked over my grave." This saying is traditionally said after someone experiences random shivering; it is derived from folklore of the Middle Ages, when people believed the veil between the living and the dead was very thin.
In Aunt Alexandra's case, this expression seems to be an exclamation of prescience; without knowing it, she is anticipating that something awful will happen later that night. It is Halloween and in order to keep the children out of trouble, the ladies of Maycomb have organized a carnival at the school. Scout has been recruited to play a ham in the pageant organized by Mrs. Merriweather. Although an adult would normally escort the children when they leave the house after dark, Atticus "couldn't stand a pageant" after his Montgomery excursion and Aunt Alexandra is too tired after spending the afternoon decorating the stage.
Thus, the two children begin their "longest journey" when they walk home alone later that night and are violently attacked by Bob Ewell in the dark. Aunt Alexandra's comment seems to predict this near-death experience, and it also harkens to the theme of superstition that appears throughout the book, particularly around the approach of death.
Tom Robinson has been killed and Bob Ewell has been terrorizing the people he holds responsible for defending Tom. He has set his sight on Atticus now and knows the only way to get to Atticus is through his children.
When Aunt Alexandra says that someone just walked over her grave, she is referring to the old folklore that says when you get a chill it means someone has walked over your grave. This superstition has been around for centuries. Aunt Alexandra says she has an uneasy feeling about sending the kids out on their own. Jem and Scout have gone be themselves to the school for the Halloween pageant. Atticus would have usually been the one to walk them to the school, but he has just returned from Montgomery and is tired. Aunt Alexandra senses that something is wrong. The theme of her saying this, is that it is a foreboding feeling and she knows something bad is going to happen. It is a foreshadow of the events that are about to take place. Jem and Scout are in great danger and their lives are in danger. Bob Ewell is following them and planning to take out his revenge on Atticus by doing something to his children, and Aunt Alexandra is aware that something bad is about to take place.
"Someone is walking over my grave" is an old expression that is usually made in "response to a sudden unexplained shudder or shivering." It is similar to "goose pimples" that one gets when startled or from sudden coldness. Although its origins are much older, the saying can be traced to the 18th century writer Jonathan Swift. The actual "chill" that one gets is believed to be from "a subconscious release of the stress hormone adrenaline."
In Aunt Alexandra's case, it came from having "a pinprick of apprehension" about Jem and Scout going unescorted to the Halloween pageant. Both Alexandra and Atticus had decided not to go--Atticus would usually have walked the children to the school after dark--since they were both tired: Atticus had just returned from Montgomery, and Alexandra had spent the afternoon decorating the school stage for the event. Thematically, Alexandra is adding a superstitious twist to the story, since superstitions are mentioned at the beginning of the following chapter when the children walk down the eerie pathway past the Radley house to the school. As for the plot, Alexandra's expression foreshadows the nearly tragic events that unfold on the children's walk home.