In Chapter 13, Holgrave reads aloud his fictionalized story of Alice Pyncheon, the woman after whom Alice's posies are named. The chapter functions as a flashback to an earlier point in the Pyncheon and Maule family history, and it also establishes that Hawthorne is using the main plot of the book as a frame story for a broader collection of lore (including the lore about Alice and her death).
Holgrave frames the story itself as neither truth nor fiction, but somewhere in between. In Chapter 12, just before he starts reading it to Phoebe, he tells her:
I have put an incident of the Pyncheon family history, with which I happen to be acquainted, into the form of a legend, and mean to publish it in a magazine.
Holgrave bases his story on a real "incident of the Pyncheon family history," but he puts it "into the form of a legend." As he goes on to boast, his writing is "as provocative of tears as an onion." Hawthorne himself has stated in his preface and at various points throughout the book that he is interested in taking bits of history and relating them in a way that is not confined to facts but nonetheless contains some kind of emotional truth for the reader. Holgrave seems to have the same philosophy on writing. For Phoebe, who is learning about the Pyncheon family history, the story functions as a flashback to the days when Alice Pyncheon (a figure who has much in common with Phoebe) was alive. It satisfies her curiosity about this ancestor of hers, and it so fully captivates her attention that she is in something of a trance when Holgrave stops reading in Chapter 14.
Because Holgrave's philosophy on writing is so similar to Hawthorne's, the reader can recognize that Hawthorne is using the "flashback" to nest another romance within the romance he is writing himself. Holgrave is a fictionalized Hawthorne, researching a segment of the Pyncheon family history and turning it into a "legend" to be sold in a magazine.
Holgrave's story allows Hawthorne to explore, at a remove from himself, the idea of mesmerism. Hawthorne himself did not hold much stock in mesmerism or witchcraft. He generally includes a scientific explanation for the fantastical, even while describing the illusion of fantasy science can sometimes create. For instance, the Pyncheons are not really cursed by Maule; they simply have a congenital disease that causes them to die in a dramatic way that looks as though they are suffering from Maule's curse. But within the frame of Holgrave's story, Hawthorne conducts a sort of thought experiment about what mesmerism might look like if it were real. The frame story allows him not to explain what really happened to Alice because it is not "his" story, but Holgrave's.