When Anne gives everyone presents at Hanukah, this shows that she is beginning to empathize with others’ feelings.
The presents that Anne gives the residents of the Annex demonstrate her empathy and deep understanding of human nature. She gives each person something meaningful in the form of gifts she makes herself. This includes erasing all of the answers in a crossword puzzle book for her sister, making a cigarette for Mr. Van Daan, and giving her mother a coupon book promising to do what she is told.
Dussel. You wouldn’t want to sell that, Mrs. Frank?
Mrs. Frank. Never! This is the most precious gift I’ve ever had! (Act 1, Scene 5)
Anne gives each person a thoughtful gift, and this demonstrates that she is getting more mature and thinking about her effect on other people. Anne was always sensitive to her own feelings, but this scene shows that she is beginning to think about the feelings of others as well.
It is no coincidence that this scene appears at the end of Act 1. In Act 2 we see a more mature and more responsible Anne, who is growing up and beginning to be a young woman.