What is the significance of the ending of A Doll’s House (With respect to the author’s choices)?

At the end of the play, Nora Helmer makes a radical decision to leave her husband, Torvald, and her children in order to live independently of society's expectations for women and discover who she really is. She tells her husband,

Our house has been nothing but a play-room. Here I have been your doll-wife, just as at home I used to be papa's doll-child. And the children, in their turn, have been my dolls. I thought it fun when you played with me, just as the children did when I played with them. That has been our marriage, Torvald.

She realizes that she was the plaything of her own father and has since become the plaything of her husband. She is not respected as an individual with personal wants, intentions, and goals. Instead, she is simply expected to fulfill her role, first as a dutiful and obedient daughter and next as a dutiful and obedient wife. Not only is Nora's realization significant, her willingness to strike out on her own in order to discover her sense of self is, in abandoning her family, also quite significant because, at the time, such an action would have been very rare. Nora is essentially giving up her place in society by refusing to follow society's rules for women of her class. She says,

I must stand quite alone if I am ever to know myself and my surroundings; so I cannot stay with you.

Her choice is radical, and it was actually quite controversial at the time of the play's initial performances—one actress actually refused to perform the role as written and insisted on a different ending for a few performances (until she realized the original was better). The radical nature of the choice makes it significant.