What does the loan show about Nora?

Nora's taking out the loan demonstrates that she loves her husband unselfishly and has the courage to do what is necessary for his welfare.

In Act I Nora talks with her old friend, Christine Linde, who is widowed and has returned to the town to find work. As they converse, Mrs. Linde seems to think that Nora has led a soft life, but Nora contradicts her, saying both she and Torvald have had to work hard; in fact, Torvald worked so hard that he became seriously ill, and the doctors urged him to travel the Southern Europe. Mrs. Linde asks if Nora and Torvald went to Southern Italy.

NORA. Yes, we did. But you won't believe how hard it was to get away....But of course we had to go. Oh, it was a wonderful trip. And it saved Torvald's life. But it took a lot of money, Kristine. 

When Nora is rather vague about how she obtained the money for the trip, saying merely that her father helped her, Mrs Linde thinks Nora received the money from her father, Nora contradicts, saying that she has raised it herself. Further, she proudly explains how with fierce determination she has paid the money back by doing small jobs. Yet, there is some mystery to how Nora could obtain so much money on her own.

Much later, as Torvald learns that Nora risked breaking the law by forging her father's name on the loan so that she could save her husband, Torvald is unforgiving and appalled that she could do such a thing and bring shame to his name. Moreover, his myopic and selfish reaction to learning of Nora's ill-gotten loan acts as the catalyst to Nora's awakening about their relationship: While she has been the loving and unselfish wife, making great sacrifices so that Torvald's health be restored, he, on the contrary, has been self-centered, perceiving Nora merely as his "doll," and when she breaks from this mold, he is unforgiving.