Nora's role in the household is well-defined, at least from Helmer's point of view.
According to her husband, Nora is supposed to look after the children, give instructions to the hired help, and generally look after the home. She should defer to him when making decisions about money and should also adopt his opinions as her own (even in matters of child rearing, if it comes to that).
Interestingly, Nora's role as a woman in the household is largely defined by her husband and not by her own agency, sensibilities or speech. (This fact is what she eventually rebels against at the end of the play.)
These views are indicative of a social atmosphere characterized by a somewhat rigid morality (as also seen in the disapprobation heaped on Krogstad when he commits forgery), but they are made particularly concrete in Helmer.
"In the nineteenth century, women's lives were limited to socially prescribed behaviors, and women were considered to be little more than property; Nora embodies the issues that confronted women during this period" (eNotes).
Helmer stands as a figure painfully aware of social norms and or public opinion, afraid to lose his reputation and quick to judge others for failing to live up to generic social expectations. His relationship to his wife, in its many aspects of intellectual and social power, notably parallels the relationship that Nora shared with her father. The patronizing nature of the father-daughter relationship (justified, perhaps to some extent, by literal patronage/parenting) is repeated in Helmer's treatment of his wife.
In these ways, one meaning of the title of the play becomes clear. Nora is Helmer's doll. She is to do what he says, dress nicely in the clothes he buys for her and so perform his ideal of feminine passivity and beauty. The dynamic between Nora and Helmer (again from his point of view) is repeatedly made overt through his many diminutive nicknames for his wife.
Nora is his “singing lark,” his pretty “little squirrel,” and his “little spendthrift" (eNotes).
Although she is expected to be passive and obedient, Nora acts rashly and takes charge of decisions for herself. Her rashness can be seen, perhaps, as a response to the knowledge that she must always assert herself secretly and avoid letting her husband know that she has acted decisively on her own.
In choosing to forge a signature, Nora commits a crime and also saves her husband's life. He was ill and failing to recover and so she took matters into her own hands to rescue him from illness. This act also demonstrates her power - - the power to be the strong one in the relationship, the power to make up her own mind. Due to her husbands strong and narrow views on the role Nora is supposed to play, Nora must keep her power a secret. Thus she tacitly agrees to be powerless in the relationship. Only by breaking from her husband can she claim authority over her own identity.