Fitzgerald's "Babylon Revisited" is significant as it is a clear example of the Modernist time period. This period is considered to have taken place between the years 1900-1950. During this time, several world and U.S. events occurred that shook the very foundation of authority, tradition, and both social and individual identity. Examples of these events include the two World Wars, the Jazz Age, the Harlem Renaissance, the Stock Market Crash, and subsequently, the Great Depression. Charlie Wales, the protagonist of "Babylon Revisited," is an example of a modernist man. He lived during the Jazz Age, in which he partied lavishly and wasted money like it was growing on trees. After the Stock Market Crash, however, he was back to square one. He had to not only pick up the pieces of his financial losses, but of his broken personal life as well. This was common of many people during this time period. Fitzgerald would have known this all too well. 

The person who previously answered your question provided a fine summary of the story’s plot and a good overview of some of its major themes.  I will therefore focus on one representative passage from the story and try to discuss some significant aspects of that passage.

At one point in the middle of the story, Charlie happens to use the word “damn” during a discussion with his bitter sister-in-law, Marion, who blames Charlie for the death of her sister, Charlie’s deceased wife.  Marion tells Charlie not to swear at her, prompting Charlie to consider the situation in which he and his daughter find themselves:

Charlie became increasingly alarmed at leaving Honoria in this atmosphere of hostility against himself; sooner or later it would come out, in a word here, a shake of the head there, and some of that distrust would be irrevocably implanted in Honoria. But he pulled his temper down out of his face and shut it up inside him; he had won a point, for Lincoln realized the absurdity of Marion's remark and asked her lightly since when she had objected to the word "damn."

This passage is significant for a number of reasons, including the following:

• It implies Charlie’s sense of powerlessness, a major theme of the story. He cannot undo what has happened, and he is literally at the mercy of the angry Marion.
• It exemplifies how important regaining Honoria now is to Charlie. Indeed, it regaining her is his major motivation and goal.
• It emphasizes Charlie’s sense of loneliness, another important theme of the story.
• It emphasizes Charlie’s fear that he may become even lonelier if Marion can turn Honoria against him.
• It illustrates Charlie’s efforts at self-control; he pulls his temper down in the same way that he tries to control his alcoholism.
• It illustrates the idea that Charlie’s relations with Marion are a kind of muted, implicit combat, with Marion as the aggressor.
• It reveals that the significantly-named Lincoln is fair-minded and thus may prove a valuable ally in Charlie’s skirmishes with Marion.
• It raises the possibility that although Marion is powerful now, she may lose her power through the kinds of foolish remarks she has just made.  This episode thus adds to the suspense of the story, raising the real possibility that Charlie may indeed someday soon regain his lost Honoria.

All the themes, motifs, and techniques just discussed are relevant to, and present in, the story as a whole.