The death of Mrs. Radley is important for two reasons. First of all, it reveals the distinct social and cultural hierarchy that exists in Maycomb. The Radleys are looked down upon by respectable society on account of their religion as "foot-washing" Baptists. This makes them a class apart, widely excoriated as religious fanatics and extremists. As such, Mrs. Radley's death is generally treated with indifference by the local townsfolk. They never knew her, on account of her social isolation; but then, they never wanted to know her, either.
Secondly, Mrs. Radley's death highlights just how the Radley family remains a source of mystery and local legend to the townsfolk, especially to the children. At this stage in the story, Boo Radley is still Maycomb's resident boogie man to Scout and Jem. They still see him as that weird, creepy guy who once stabbed his old man with a pair of scissors. So they're more than a little disappointed to learn that Mrs. Radley actually died of natural causes; it spoils the rich fantasy world they've built around Boo.
At the beginning of Chapter 8, Mrs. Radley dies of natural causes. Scout mentions that her death had a small effect on the community of Maycomb and people hardly noticed. The Radleys were "foot-washing Baptists" who did not socialize with their neighbors like the majority of citizens in Maycomb. Scout says that the only time the neighbors saw Mrs. Radley was when she was watering her cannas. Scout and Jem are upset when Atticus tells them that she died of natural causes. They figured that Boo Radley had finally killed his own mother. At this point in the novel, Jem and Scout are still under the impression that Boo Radley is a violent individual who wreaks havoc throughout the neighborhood and is capable of harming his family members.