It is  not actually the lady who brings the grapes that says anything to give Digory hope, but his Aunt Letty. Aunt Letty looks after Digory's mother Mabel who appears to be terminally ill. Letty remarks: 'What lovely grapes!' and goes on:

I'm sure if anything could do her good these would. But poor, dear little Mabel! I'm afraid it would need fruit from the Land of Youth to help her now. Nothing in this world will do much.

These words give Digory hope that his mother might be cured. Thanks to some magic experiments conducted by Uncle Andrew (a rather odious character) he has actually visited other worlds, and knows that they really do exist. His aunt's remarks set him hoping that there really might be a 'Land of Youth' somewhere which might hold a cure for his mother. He decides to go looking for it. In the event, he and his friend Polly end up in the wonderful land of Narnia, created by the great Lion Aslan. In this new, young world he does indeed find an apple which heals his mother. In the process, though, he also has to face up to the evil witch Jadis whom he inadvertently brings along, first to our world, and then to Narnia, from her own ruined world of Charn.

The portrayal of Digory's dying mother, revived by a fruit from another realm, is especially moving when we remember that C.S. Lewis' own mother died of cancer when he was only a child.