Phoebe is a country cousin of Hepzibah and Clifford. She's the daughter of someone named Arthur (a brother of Hepzibah and Clifford's, maybe?). So she's a Pyncheon, but she's been raised blissfully far away from the gloomy influence of the House of the Seven Gables. She is aware of the old Pyncheon story of Maule's curse, but she doesn't worry about it too much.
Because Phoebe hasn't grown up with too many high-flying ideas about the Pyncheon family, she is willing to throw herself into work without worrying about whether it's ladylike or not. When she arrives at the House of the Seven Gables looking for a place to stay (because her father has just remarried), she starts helping out right away, both in Hepzibah's shop and in the house. Phoebe soon becomes the life and soul of the House of the Seven Gables: her presence helps keep both Hepzibah and Clifford strong enough to break at least a little bit free of their deep miseries. (Check out "Quotes: Gender" to see some closer analyses of the importance of Phoebe's place in the home.)
Clearly Phoebe is Hawthorne's idea of the perfect woman. She is pretty, talented, and diligent. She loves keeping house and she makes hard work seem easy. The narrator describes Phoebe as "the example of feminine grace and availability combined [...] where ladies did not exist" (5.43). In other words, she's womanly and available to work, and she doesn't fret over not being a "lady" by birth.
This makes Phoebe not only an ideal woman in general, but also a perfect American woman. Phoebe is part of a new "republican" (2.14) (as in democratic) spirit of womanhood, in which girls will do their bit to support themselves with grace and spirit. By contrast, Hepzibah's feelings about the importance of being a gentlewoman are "the shadowy food of aristocratic reminiscences" (2.13) and not suited for our modern times. The difference between Phoebe and Hepzibah isn't just one of personality or appearance; it's also a profound generational shift.
Phoebe represents the healthy virtues of contemporary American society – as Hawthorne imagines them, at least. She is energetic, hardworking, and faithful. She goes to church every Sunday and believes absolutely in obeying rules and upholding the law. She initially mistrusts Mr. Holgrave because Hepzibah has told Phoebe that he's a wild shaking reformer. Phoebe doesn't hold with his strange ideas about abolishing inheritances or shaking up families every 50 years. She is conservative at heart, even if she doesn't believe in the aristocratic principles that a truly old-fashioned woman like Hepzibah holds dear.
Phoebe has excellent instincts. At her first meeting with Judge Pyncheon, when she thinks he is just a harmless elderly relative of hers, he leans over to kiss her. Without really knowing why, Phoebe immediately starts back and won't let him touch her. She also thinks Judge Pyncheon looks exactly like the stern portrait of Colonel Pyncheon, even though when she takes a second look, they don't seem so very similar on the surface. So Phoebe knows more than she knows she knows.
Phoebe and Mr. Holgrave wind up together. Even the narrator admits that this was probably inevitable because they are around the same age and have no one else to hang out with: "The only youthful mind with which Phoebe had the opportunity of frequent intercourse was that of the daguerreotypist" (7.5). (Here intercourse just means conversation – no hanky-panky intended.) Phoebe finds Mr. Holgrave off-putting and distant to start with, and Mr. Holgrave thinks Phoebe is kind of dumb. But eventually the weirdness of the experiences they share leads Mr. Holgrave to tell Phoebe he loves her, with the dead body of Judge Pyncheon in the next room. (Because that's romantic.)
Whether or not you actually buy the love story of Phoebe Pyncheon and Mr. Holgrave, it's pretty much necessary to the plot. Phoebe is basically Alice Pyncheon reborn, and Mr. Holgrave is a descendent of Matthew Maule. By marrying Phoebe and mingling their families, Mr. Holgrave can symbolically undo Maule's curse on the Pyncheon family line.
What's more, Phoebe and Mr. Holgrave can rewrite the story of Alice Pyncheon and Matthew Maule II. Matthew Maule II, caught up in his vengeful spirit and desire for power, humiliates Alice Pyncheon to death with his hypnosis. Mr. Holgrave holds the exact same power over Phoebe (literally, as she sits in front of him in a trance after he reads his story to her in Chapter 13) but he decides to let her go free. Mr. Holgrave forgives the Pyncheons on behalf of the Maule line, and Phoebe shares Judge Pyncheon's inheritance with her future husband. All the historical injuries they've been working through seem cured.