Rosemary is Jacob's favorite nurse at the retirement home and the only one who really treats him with respect. She gives him real food when he asks for it, listens when he talks, and treats him like he still has some dignity left. Other people who work at the home treat Jacob like he's a little boy or somehow incapacitated just because he's elderly. Not cool, other people.
Rosemary's kindness extends to other people at the home as well. Here's what she tells Jacob to make him feel better about his encounter with McGuinty:
Sometimes when you get older – and I'm not talking about you, I'm talking generally, because everyone ages differently – things you think on and wish on start to seem real. And then you believe them […]. (13.68)
Jacob is experiencing the kind of aging and questioning of reality that Rosemary is talking about here. Even though Rosemary is younger than him, she has a perspective on aging that he doesn't. Rosemary seems young to Jacob, but she has a whole family of her own and is getting on in years herself.
Conveniently, Rosemary's name is similar to another name that's important to Jacob: Rosie. At one point in the book, Jacob even calls Rosemary Rosie as he's recalling a moment from his past. It's probably no coincidence that the names Rosie and Rosemary are connected with the idea of remembering. Think of what Ophelia says in Shakespeare's Hamlet: "There's rosemary, that's for remembrance" (Act IV, Scene V). And there's that old saying that elephants never forget. Can't get more clear than that.
Jacob does a lot of remembering in Rosemary's presence. Ironically, he even talks to her about his past and then realizes he has no memory of that conversation. He's embarrassed, telling her:
No. About … Oh hell, don't you understand? I didn't even realize I was talking. It's the beginning of the end. It's all downhill from here, and I didn't have very far to go. But I was really hoping to hang on to my brains. I really was. (16.19)
But Rosemary soothes him, as she often does. (For more on the importance of memory, check out the symbols section on "Elephants.") And Jacob reveals just how important Rosemary is to him when he learns that she's leaving the nursing home. Without her there, he really has no reason to stay. So, hey, why not join the circus?