This is a bucolic (pastoral) story, in which the characters are representative of the era, in fact, they are meant to be described as if hey were parts of a post card.
The plot basically rounds about the central theme: Change and Progress.
The character of Fancy Day represents the new, and the potentially more fanciful and interesting things that occur in places outside the country. Her entrance into the daily routine of these very country folks means the beginning of the changes that are coming to the town.
The fact that so many men are flirting with her and she with them is also representative of perhaps the curiosity that these folks feel about change. She basically plays and flirts with all of them and gives them false hopes. She even accepts a marriage proposal from the vicar while she was engaged to Dick, and she was also flirting with Frederick, the rich man, during this time. So, as far as Fancy Day, her role in the story is to represent how the countrymen sudddently were in touch with change.
As far as the most important moment in the story, it is when the very traditional and always-there choir receives the news that they are to be substituted with an organ and that Fancy May, of all people, will be the one playing it. Hence, not only did Fancy come to change things, but she IS change, and that is what makes her so forbidden, mysterious, yet, curious, and desirable.
The most poignant and telling detail is the phrase "You can't stand in the way of progress" which is what embodies the theme of the story.