For the protagonist Holden Caulfield, in the novel The Catcher in the Rye, objects mean more to him than that of human relationships. Holden holds onto Allie's baseball glove because he knows it is representative of his brother (Allie has died and it is all Holden has left). The record, "Little Shirley Beans," is no different.
For Holden, the album represents his hope that his sister, Phoebe, will remain innocent. When watching Phoebe on the carousal, Holden breaks down. He knows that she is growing to grow up and he fears this. Holden's obsession with phonies rules his life. Holden is afraid that if Phoebe grows up, without him there, she may become a phony.
The record, therefore, allows Phoebe to possess something that will remind her of Holden after he is gone--much like Allie's mit is a reminder for Holden. It is Holden's hope that the record will remind her of Holden and she will not become something he hates.
The Shirley Beans Record represents a world without phoniness. Holden mentions the fact that he hates phonies several times in the book, and when he first talks about the record he mentions the fact that he enjoys the singer’s voice, and how she doesn’t sing in an overly cutesy way, as some children would. The breaking od the record might symbolize the fact that he himself has become a phony.