The title of the story is a clue to the mood of the novel. Post World War II Japan is a time when the people who supported the imperialistic government during the war must assess and try to come to terms with what their country and they themselves did. It's a time of change and uncertainty. Masuji Ono, the narrator, is uncomfortable with the changes in 1948, but he's also concerned about his past and the part he played in allowing the government to use his art in their propaganda. The mood created is one of uncertainty and a feeling of being uncomfortable with the past and the present.
Before the war, the "floating world" was the underworld of the artists and geishas, representing decadence and idealism. Post-war Japan is now a "floating world" because it isn't stable; it's in a state of flux, changing the values and traditions of its society. This is clearly seen at the end when Ono is ready to admit to his future in-laws that he was wrong to support the imperialist government. It is then that he's told that what he did in the war isn't relevant or important to the marriage. The older generation is being replaced with the new values of the younger generation, and Ono is able to come to terms with his past.