The great change that takes place in Nora is a development of identity. Nora begins the play as a person without her own opinions. She ends the play as a person dedicated to defining herself as an individual, willing to make great sacrifices to do so. 

Nora's husband, Torvald, provides Nora with her only definition early in the play, characterizing her as a "singing lark", a "little squirrel" and otherwise diminutive and without agency.

She is viewed as an object, a toy, a child, but never an equal.

This uneven relationship is never more clear than in the scene when Nora prepares for the dance and preens for Torvald, manipulating him, and being characterized diminutive by him throughout.

The actions Nora takes throughout the play (until the very end) are kept secret. She sneaks cookies. She secretly takes a loan and suffers Krogstad's blackmail. These actions, as secrets, cannot actively define Nora or build an identity for her. 

After being disappointed by Torvald's reaction to the news of Krogstad's blackmail, Nora finally comes to realize that she has no identity of her own. Torvald berates and belittles her instead of fulfilling her vision of him as noble and loving. 

Nora is little more than a child playing a role; she is a "doll" occupying a doll's house, a child who has exchanged a father for a husband without changing or maturing in any way.

The hope that Nora has invested in Torvald gives way to the realization that he does not respect her and that, perhaps, she is not enough of a person to deserve respect. 

When Nora finally gives up her dream for a miracle and, instead, accepts the reality of her husband's failings, she finally takes her first steps toward maturity.

Nora's change receives quite a bit of commentary in the last scene of the play. Her realization is fully articulated, as is her plight in marriage with Torvald (a complete lack of identity of her own). 

She is willing to give up her children, ultimately, so that she can cease to be a child herself and learn to develop her own ideas and opinions.

How has Nora changed from the beginning of the play A Doll's House to the end? How has Torvald?

Nora has already started changing by the time the play begins. She has been married to Torvald, and their union is not an equal one. Despite Nora's intelligence and passionate nature, he patronizes her and she plays along with the game because she initially takes pleasure in being like a little "doll" for him to play house with. However, deep down Nora craves responsibility and selfhood. She has taken out a loan with the help of Krogstad to save Torvald's life without his knowing about it. When circumstances lead to Torvald discovering the truth, he becomes furious and berates Nora.

This negative reaction is what causes Nora to change from the passive, submissive person she had forced herself to be while married to Torvald. She realizes she is expected to act like an overgrown child, completely reliant on her husband, and she leaves him so she can find herself, telling Torvald that "I’m no longer prepared to accept what people say and what’s written in books. I must think things out for myself, and try to find my own answer."

Torvald also undergoes a change in that his perception of the world falls apart. He believes women must rely on men and that their primary roles are as wives and mothers. He prides himself on being a model man: successful in business, dominant at home, and free from any kind of debt to anyone else. In his own way, he too is "performing": if Nora is pretending to be the perfect image of a Victorian wife, then Torvald is pretending to be the perfect image of a Victorian husband. However, his hyper-masculine image of himself turns out to be an illusion: Nora took out a loan behind his back so she could take him to a warmer climate when he was ill. This infuriates him, as it is a challenge to his control over Nora and it makes him dependent on another, but when Nora goes to leave him, Torvald begs her to stay, signaling a shift in power in their relationship.

While Torvald does oppose Nora's final liberation, he too undergoes a liberation and major character development. His last line where he wonders if "the most wonderful thing of all" could truly happen offers the audience a cautiously optimistic possibility: that Torvald and Nora might both be able to reunite one day as equals, both of them changed people.