The above passage suggests about the relationship between daisy and Mr. winterbourne that they do not share a sweet relationship and have some bitter attitude towards each other. There are secrets which are kept and a certain kind of situation is being awaited for the specific secret to be revealed. The way daisy speaks is not referred to as polite or so. There are ideas and thoughts which are developed for or against each other.
In this passage, we see that Mrs. Miller communicates a message from Daisy to Mr. Winterbourne. Mrs. Miller says that Daisy was very insistent about the importance of the message. She wanted Winterbourne to know that she was never engaged to anyone else. What this passage suggests is that Daisy did in fact loved Winterbourne, and that the plot she faked with the Italian man was only a strategy to make him jealous. Moreover, as Daisy wants Winterbourne to think about the times they had in Switzerland, she most likely is thinking about them too, which shows that she is still in love with him.