The last section of part three is important to understand the development of the novel, Eilis's mood and for the comprehension of future events.
There are multiple reasons for the section to be particularly significant.
First of all, there's Eilis's telephone conversation with her mother, followed by the implication of the news of Rose's death in her relationship with Tony, her boyfriend, to continue with the content and the effect of Eilis's brother's letter, and last but not least, the consequences of Father Flood's opinion where the two characters are shown in action.
Right from the start of the protagonist's phone call with her mother, the reader notice that it is all written though the showing technique. According to that choice, the reader feels involved because it has been given him the possibility to know in what exactly consist exchange dialogues between the two characters. However, analyzing this part is significant because it is the first dialogue not to be filtrated. Indeed, thanks to sentences such as: " I went in to call her and she was fast asleep and I said I had to leave her. But I knew as I went down the stairs. It wasn't like her to sleep in like that. I looked at the clock in the kitchen and I said I would give her ten minutes more and then when I went up and touched her she was stone cold" [...] "I whispered and act of contrition into her head. Then I ran next door." [..] "She must have died in her sleep" the narrator conveys the incredulity of Eilis and her mother about the news. In addition, Eilis feels completely lost. She is actually living in a word that does not belong to her, nor she feels at home. Last but not least, she has just lost forever her idealized mainstay.
Going on reading, it goes without saying that the protagonist tells the tragical fact to her boyfriend, Tony. Firstly, it seemed that he does not give so much attention. Ex: "Eilis wished Tony would stop accepting further sandwiches and cakes from Mrs Kehoe and thanking her from being so kind. She wanted him to leave and Mrs Kehoe to stop talking with Father Flood as well. [...] Mrs Kehoe, Father Flood and Tony spoke as though she was not there, going over the changes that had occurred in Brooklyn in the past few year and offering their opinions on what further changes might occurred. However, after that scene he seems to be very interested, sensitive, intentioned to give her and helping hand. ("I'll help you if you like."). On the other hand, Tony begins to be scared of Eilis's return to Ireland. He does not completely rely on her. Owing to his shy, unsure and instinctive personally, he decides to ask Eilis to marry him. The decision completely shocks bit the reader and Eilis, that gets carried away and accepts. This is just an anticipation that will help the narrator to convey the ambiguous ending.
Later on, the novelist reports a crucial letter written from Eilis's brother to her. To tell the truth, the letter is just a pretext to convey Eilis feeling of nostalgia, guilt and homesickness, making clear to the reader the protagonist's conflicting emotions.
Consequently, the letter is juxtaposed to the young adolescent's dialogue with Father Flood, the priest that made the American dream true. Indeed, it can be said that he represents the mediator between Ireland and Brooklyn. He succeeded in planning the logistical matters for Eilis's departure. So that, she decides to return to Ireland.
To conclude, you can state that all that said introduce and leads to the fourth part, the last one.