The unclouded knowledge of the self refers to a state of mind where an individual, in this case Nora, has reached a point where there is no doubt on her mind about who she is, what she wants, and how she has reached the point in life to which she has arrived.
This moment comes to Nora later on in life, after she married and had children; after she had spent all her better years trying to please a superficial husband, and after playing the role of the ever-entertaining doll to the rest of the world.
If we go back into Nora's time-line, we realize that, ever since she was very young, she had been a sort of "play thing" for her own father. As a result, she began to believe that she was, indeed, a play-thing so she acted just like that. When she married Torvald, she perpetuated this silly behavior and made it into her trademark, always ensuring that her husband gets a good laugh, or at least a good chuckle, even if it was at her expense. All this time she had believed that her act was real and that, by acting like a "doll" she was actually making people happy. Little did Nora know, that her act was for herself only; Torvald was always too busy to notice anything in Nora BUT her act, and the rest of the world seemed to just ignore her.
The fact that she was so continuously ignored may have led Nora to the realization that she wanted to do "something" great and magnanimous. Her Magnum Opus, so to speak, was borrowing money from a man who is not her husband (a social no-no) to be able to afford medical treatment for Torvald. Ever since she made this choice, she knew that this social indiscretion could always be forgiven because her husband would understand that, ultimately, it was a choice made out of love. When the moment of truth comes and Torvald finds out about what Nora did, his words were insulting, depressing, and far from understanding.
you have destroyed all my happiness.. I am in the power of an unscrupulous man.... And I must sink to such miserable depths because of a thoughtless woman
These and many more words slapped Nora into reality. as she sits there now, listening to her husband insult her kindness she realizes who she is, and how distanced this woman that she actually is happens to be from the one she pretended to be. Nora is now officially "unclouded" of the knowledge of herself; she has finally developed into maturity. Nora has finally grown up.
The result of this discovery is her immediate decision to remove herself from the household, and leave everything, even the children, behind. The realization of having played a silly role for the benefit of others has made her reality way too harsh to bare. The woman who had sacrificed, who had loved, and who had lost is now who stands in front of Torvald; not the little doll that he thinks that she still is.
Her thoughts become solidified in the uttering of these words:
...our home has been nothing but a playroom. I have been your doll-wife, just as at home I was papa's doll-child; and here the children have been my dolls... That is what our marriage has been, Torvald.
Therefore, as Nora's former emotions, ideas, and suppositions finally leave for good, she gets the first real glimpse of herself and her reality. This is how that unclouded knowledge helps her move forward toward maturity.