Grace Cahill is Amy and Dan's beloved grandmother. Well, she was before she dies in chapter 1 and sends Amy and Dan on a race around the world without any warning. They seem to be a little bitter about that, often lamenting the fact that she hasn't left them any tricks or hints to give them an edge. Still, they have fond memories of her, and it's devastating to them when her mansion burns to the ground, destroying all the physical reminders they had of her.
Since Grace dies in chapter 1, it's hard to get a bead on her personality. We know she doted on Amy and Dan, but she also kept huge secrets from them. She never even showed them pictures of their parents: "Grace always insisted she had no photographs of them, though Dan never understood why" (6.87). It's more than a little strange that she wouldn't have photos of her own daughter. Could she be hiding something?
Before Grace's death, we see her making the conscious decision to change her will. By doing this, she's unlocked a great secret that will make someone the most powerful person in the world. It could be someone good, or someone evil. She seems to be doing it for Amy and Dan, thinking that if "they don't succeed […] five hundred years of work have been for nothing. […] The family, the world, all of it" (1.11). She doesn't explicitly say Amy and Dan, but who else could this mysterious "they" be? And why is Grace even allowing the option for this secret to fall into the wrong hands?
We learn throughout the book that most of the Cahills are scheming and manipulative. We hate to say this about such a sweet old lady after her death, but we're afraid Grace might be exactly the same as the rest of them.