Other than being Bapaji's right-hand-woman, Hassan says that he "cannot give her enough credit" (1.17) for what happened to him. He calls her "my Ammi" the first time we hear about her, which gives us a good idea about how he feels about his grandmother. He also remembers following her fabulous cooking around when he's a little kid.
Ammi's the one who experiments with the recipes for the American and British soldiers, which makes Bapaji successful, and her cooking standard is something that Hassan looks up to for the rest of his life. Considering the heights he soars to, this is really saying something about this woman's culinary skills.
Ammi continues to be a part of the bandwagon long after Bapaji passes away. She has a sharp tongue and kind of a my way or the high way personality. Case in point: She's often shown screaming and yelling in the kitchen while in the middle of a bunch of different things.
As Ammi gets older, she becomes more and more eccentric. The first example of this is when she starts pulling her hair out (literally) after Mummy's funeral, and when the Hajis move to London, she begins to suffer from dementia and the family has to keep a close eye on her. We don't hear when she dies exactly, but for most of the book the family all keeps an eye on her as she wanders around with her sudden outburst of odd behavior.