Sissy is the daughter of a circus performer, who comes to live with the Gradgrinds as a servant when her father abandons her. She is naturally good and emotionally healthy, so the Gradgrind philosophy doesn't affect her, and she is able to take care of Louisa and to arrange Tom's escape. At the end of the novel, she is the only character who gets a happy ending of marriage and children.
Sissy is the main force for good in the novel. She is kind, caring, and loving. In the face of being abandoned by her father and then being forced to learn the Gradgrind philosophy, she never stops being the only grounding, emotionally positive force in Coketown. In a way, she is similar to another one of Dickens's favorite character types, the perfect young woman who selflessly takes care of other people. Check out Esther in Bleak House, Amy Dorrit in Little Dorrit, Lizzie in Our Mutual Friend… OK, there are a lot of them. Take our word for it.
But in this novel, Sissy is also a messenger from the land of imagination, creativity, and selfless actions. For instance, all three are combined when she cheers up her father after a hard day in the circus ring by reading him fairy tales about ogres and giants. What's more, everyone else in the novel is so weirdly screwed up, that the reader is always hugely relieved whenever Sissy appears, because finally someone normal is going to say some normal things in a normal way about all the craziness going on.
And yet Sissy, like Bounderby, is an interesting contradiction. She is obviously tied to the circus, to entertainment, to the life of the imagination. But she is also clearly one of the more realistic and matter-of-fact characters in the novel. The reason she can't deal with most of things Gradgrind's school is trying to teach her is that they are so abstract. Gradgrind's policies don't make any actual sense despite being logical (well, to a Utilitarianist, anyway). Think about when Sissy tells Louisa about her mistakes in school. They are all intersections of economic theory. They're clearly meant to be Sissy's more reasonable, human interpretations of what the world is actually like. For instance, when questioned about how very unimportant a few deaths in a thousand people are, she pretty sensibly answers that to the families of those dead people, those deaths are actually quite significant indeed.