The short answer is very important indeed. This is a play consisting entirely of people alienated from their true selves by the identities imposed upon them by society. The result is that no one's able to reach true maturity, kept as they are in a state of arrested development by their pre-assigned social roles.
Nora would be the most obvious example here. Her husband, Torvald, treats her like a child, feeling he has to protect her from the dangers of a harsh, unforgiving world. His condescending attitude keeps Nora in a state of prolonged childhood, denying her moral agency and preventing her from forging a life for herself outside the stifling confines of the home.
It's only when the truth of her marriage is revealed that Nora is able to take the fateful leap and slam the door on Torvald and her children. For years, Nora had been kept down through ignorance. Torvald, seeing her as nothing more than a child, consistently denied her unclouded knowledge of the world outside. Although he may have believed he was only doing this for Nora's benefit, in actual fact he was preventing her from developing as an adult. And it's difficult to see how this could possibly have been in Nora's best interests.