Boyle uses the third person narrator. The third person narrator is able to present Felicia's and the woman's (the baby sitter's) perspectives. This narrator doesn't reveal all of the thoughts of the woman and Felicia. This leaves the reader to discover how both Felicia and the woman understand each other through dialogue.
This creates an interesting parallel with the woman's quite objective descriptions of the concentration camp and Felicia's misunderstanding of them. Felicia doesn't grasp that the woman is talking about the atrocities of the concentration camp because she is too young, naive, and in her own world. The reader, however, does realize that the woman is talking about the camps from the woman's subtle hints. For example, the woman says to Felicia:
It was a camp--that was the name the place had; it was a camp. It was a place where they put people until they could decide what was to be done with them.
"Camp" is the only clue that she is talking about concentration camps. In Felicia's innocence, she thinks "camp" means something like a recreational camp or a temporary living space. The narrator does not overtly inform the reader that the woman is talking about the Holocaust and that Felicia is too young to comprehend it. This comes across through the woman's and Felicia's dialogue.
This third person point of view allows the reader to compare Felicia's and the woman's words. The reader discovers for himself/herself that Felicia, in her innocence, recognizes this woman's sorrow but puts it into terms she can understand. Felicia's own mother goes away for hours at a time but she can only have a slight understanding about what it would mean for a child's mother to leave and never return. When the woman tells her that the girl's mother never returned, Felicia still doesn't fully understand but she sympathizes with the woman's sorrow.
In this way, the narrator allows the reader to sympathize first with Felicia and then with the woman and the girl she cared for in the concentration camp. Clearly, the girl lost in the Holocaust lived in much worse circumstances. But juxtaposing the woman's story with Felicia's innocence (and misunderstanding), the reader sees the Holocaust girl's innocence in Felicia and Felicia's innocence in the girl.