Mrs. Grose is something of a blank page – a kindly, loving blank page, but a blank one nonetheless. We hear early on that she's been in the service of the family for a long time (she was a maid to the children's grandmother), and that she's deeply invested in the children. In general, she's really just a simple, kind, unquestioning soul; the Governess uses her both as a confidante and an informational tool, but Mrs. Grose doesn't ever act on her own. The Governess comments several times on the housekeeper's lack of imagination and her simplicity, marking her as a member of the stereotypical unintellectual working class (she's also illiterate).
Basically, Mrs. Grose is around to aid and abet the Governess, and turns out to be a loyal ally, albeit one that's not incredibly useful when it comes to action. Most of her significant scenes are simply discussions with the Governess, in which the latter lady gets information out of her, or confides what she's seen. It's also important to note that Mrs. Grose really doesn't want to believe that the children can possibly be at fault, and often questions the Governess's leaps in logic, until the very end, when she declares her allegiance to the Governess.