After a lot of time spent with Mr. Gradgrind's education of facts, Sissy hasn't made much "progress." One night she falls into conversation with Louisa, and bemoans how she can never answer Mr. McChoakumchild's questions the way he wants her to, though she answers the questions honestly and sensibly.
Sissy's education of fancy apparently cannot be altered. Gradgrind's education is not looking for answers that are honest and sensible—it's looking for facts, pure facts.
Their conversation turns to Sissy's parents, and Sissy reveals her mother was a dancer and her father was a clown, who read her many wonderful fairy tales and made her very happy. She also tells Louisa how desperate her father was in his misery when he couldn't please the crowds, and of his increasing depression, and how she still hopes for some word of her father. Louisa is won over, and waits as eagerly as pitiful Sissy for word of Signore Jupe (which doesn't come).
Sissy's story reveals the depth of her education in and connection to "fancy". Her parents are devoted to art and beauty and humor—to connecting with audiences and making them feel. And Sissy clearly has similar power, as her story makes Louisa feel for Sissy and to hope for the things that Sissy hopes for. Of course, such hopes lead to vulnerability, as Signore Jupe's failure to write proves. Again, though, this incident shows that Louisa does have the capacity to feel.