The significance of the title of the play A Doll's House, by Henrik Ibsen, is that it foreshadows the dynamics that take place in the Helmer household. Moreover, it also helps unveil the real role that Nora plays within her family; that of a mere entertainer to her husband and children. In the end, the title of the play becomes sort of a misnomer, since Nora actively moves away from the role of a "doll" and moves on to try to become a fully-grown, and real woman.
From the very beginning of the play, we notice how Nora's playful ways are quite enabled, and even encouraged, by her husband, Torvald. It encourages the audience to question the purpose of two adults conducting their communication in such a way. However, later we realize that this is perhaps one of the many tricks that Torvald uses to somewhat manipulate Nora's childish behavior, as well as to reinstate his role as the "man" of the house. It is a condescending way to treat people, nevertheless.
We also get to the conclusion that Nora is, essentially, a lonely woman. Torvald is obviously always working and she does a great job at keeping the image of the "cute" housewife. However, having a nurse/governess, in the house and almost nothing else to do leads Nora to be a bit of a spendthrift and to do things, albeit, silly things, behind Torvald's back.
HELMER:Don't disturb me. [A little later, he opens the door and looks into the room, pen in hand.] Bought, did you say? All these things? Has my little spendthrift been wasting money again?NORA:Yes but, Torvald, this year we really can let ourselves go a little. This is the first Christmas that we have not needed to economize
HELMER: Still, you know, we can't spend money recklessly.
However, we know that the "doll" image that Nora projects actually hides a woman that needs a lot of validation. She has never been respected for her worth as a wife and mother, but instead, gets attention by acting up and pretending to be childish. Even Mrs. Linde, her friend from many years ago, realizes this in Act II:
NORA:[...] To-morrow evening there is to be a fancy-dress ball at the Stenborgs', who live above us; and Torvald wants me to go as a Neapolitan fisher-girl, and dance the Tarantella that I learnt at Capri.MRS. LINDE:I see; you are going to keep up the character.NORA:Yes, Torvald wants me to....
Finally, Act III shows what happens when the truth about Nora's transactions are discovered, and she sees how Torvald at first is unable to see beyond the embarrassment that she causes. Later, when he sees that no harm is done and he changes his mind, she finally changes her own.
With these words, Nora finally realizes that she had been a doll to everyone she ever loved.
NORA:It is perfectly true, Torvald. When I was at home with papa, [...] He called me his doll-child, and he played with me just as I used to play with my dolls. And when I came to live with you—HELMER:What sort of an expression is that to use about our marriage?NORA:[undisturbed]. I mean that I was simply transferred from papa's hands into yours.