It's chapter 13 of Heidi, and our eponymous heroine has made her way back to her home village in the mountains after her stay in Frankfurt at the Sesemann residence. As one can imagine, the little girl is very excited to see her village and all her friends once more.
She's particularly excited to see Peter's blind grandmother, an old lady with whom Heidi had developed a deep connection prior to her leaving for Frankfurt. The old woman is overjoyed to have Heidi in her presence once more. Peter's mother, Brigitta, describes to the Grandmother what Heidi is wearing. She says she's wearing a pretty frock and has a hat with feathers in it. Brigitta asks Heidi to put it on.
But Heidi politely declines. In fact, she says that she doesn't want the hat with the feathers in it, and that Brigitta can have it if she wants. Heidi prefers to wear her old hat, as she recalls all too clearly that her grandfather once told her that he didn't want to see her and her hat and feathers again. As Heidi is incredibly anxious to see her grandfather again, she doesn't want to antagonize him. It would seem that she made the right decision to preserve her old hat.