Going off of the second educator's assessment, I think it's important to look at how jazz relates to Freud's ideas about sex.
Freud was, arguably, a proud sensualist who believed that every part of the body offered erotic pleasure. The introduction of jazz and how people danced to the music—popular dances included the Charleston and the Black Bottom—encouraged a loosening of the body. Dance partners also danced in closer proximity compared to previous eras. This greater attention to the body, women's willingness to expose parts of it in A-line dresses, and the habit of adorning their bodies with beads that offered both tactile and aural stimulation, validates some of what Freud was saying about people having a kind of polymorphic eroticism.
Freud also believed that fantasy was important to sexuality, even the presence of "perverse," or unconventional, scenarios. Arguably, Weimar Berlin has the better reputation for "loose" sexual mores compared to any major American city. However, the complexity of sexuality, which often doesn't conform to social mores, often played out in early, pre-Hays Code films, in which subjects such as infidelity and pre-marital sex were explored.
Freud's ideas fascinated much of the public in the first half of the twentieth century. That sexual desires were of greater importance than people ever realized was of great interest. By the 1920s, 1930s, and 1940s in particular, Freudian psychoanalysis permeated even the popular culture, showing up in movies and novels consumed by the general public. Most famously, a 1922 John Barrymore staging of Hamlet included Freudian interpretations of the character's relationship with his mother.
In the 1920s, Freud's ideas may not have directly caused a loosening of sexual mores—at least, not in isolation (first wave feminism and post-war reassessment of cultural values might have had more of an impact in that regard), but they did likely help some people accept these new changes, or at least, they helped explain the changes.
People were also fascinated by the idea that their own problems might be alleviated through psychoanalysis. Psychoanalysis promised a healthier mind, a very appealing notion in the optimistic America of the 1920s.
The first answer lays out some of Freud's ideas quite nicely but does not say anything about how he impacted America in the 1920s.
I would argue that most of Freud's impact came from his ideas about how central sexual desires are to human beings. He argued that many problems people have come from repressed sexual desires.
The 1920s in the United States were a time of loosening values and sexual values were loosened as well. Things that had been previously unthinkable (like women going out alone with men and like "petting" which came to be a term in those days) came to be much more accepted. You can argue that this reflects Freud's influence -- people thought that it was harmful to suppress sexual urges so much so they came to have a more open attitude towards sex.