When looking for the importance in Act One of a play, you should note the introduction of characters and the set up of a major problem which will be the main event of the play.
Act One of A Doll's House introduces:
- Nora, a seemingly flighty wife and mother who hides a secret that belies her carefree exterior
- Torvald, her husband and an up and coming banker who revels in his position at home as the king of his castle
- Mrs. Linde, the hard-working, impoverished school chum of Nora
- Krogstad, a bank associate of Torvald's with whom Nora has a secret bond of collusion
- Dr. Rank, an old family friend of Nora and Torvald's who also has a secret crush on Nora.
The main events of significance to the plot throughout the rest of the play are:
- Torvald has received a raise, which will drastically change the Helmers' financial situation.
- Nora confesses to Mrs. Linde that she has "saved" her husband by borrowing money to take him on a rest cure trip, money that she has scrimped, saved and worked to pay back. She is ecstatic that this money will now be easily paid back through Torvald's raise in salary.
- Krogstad is revealed as the man who lent Nora the money she needed for Torvald's rest cure, and he demands that she help him (by influencing Torvald) re-instate himself in his lost position at the bank or he will reveal their secret.
This last bit of information, coming at the end of the Act, is the most important for building suspense in the audience about what will happen next in the play. This is an important dramatic device, intended to hold an audience's interest during the interval between Acts.
I have provided a link below to the Enotes full summary of Act One (and analysis) for more detail.