Movies were part of the growth of mass consumer culture that emerged in the 1920s. Movies and, in particular, movie stars helped to highlight the idea of fame and celebrity. Douglas Fairbanks, Charlie Chaplin, and Greta Garbo were examples of how people became fascinated with the life of the celebrity. The movies were able to crystallize the belief of the time of self- love, as individuals were able to look at the screen, project their own wishes upon it, or project even their own sense of self upon it. Movies were able to be consumed by the people, at large, and helped to feed the belief that the 1920s was a decade of self glorification and projection of self.
Movies and radio in the 1920s also made our country more homogeneous. Immigrants assimilate into American society over time. The media of the 1920s helped to speed the assimilation for the new Americans, as well as setting us on the path to losing our regional differences.
Everyone in the country was listening to the same music, watching the same shows, identifying with the same icons. That which made us a diverse country was beginning to blur.
Movies in the 1920s came in both the silent and talking variety. The first talking movie wasn't until 1927's The Jazz Singer, so while movies in the time period were many, and were a chief source of information and mostly entertainment in the major cities, you would be hard pressed to find movie theaters in the small country towns that made up much of America.
We had our first real movie stars in the 1920s, including Clara Bow, the famous "It Girl". She was the first genuine sex symbol in American film - until the "talkie" movie because she had such a thick Brooklyn accent it didn't come across well on screen. Movies in the 20's were the beginning of the Hollywood industry.
I'm a bit unclear about your question. Do you mean, "What kind of influence did the movies MAKE in the 1920's?"
If this is your question, the movies of the 1920's served two main purposes. First some movies were pre-empted with news reels. These news reels where meant to educate people on current events. The actual movies were often for sheer entertainment. Critics of movies back then blamed producers for promoting and expanding the image and idea of the modern woman as flapper. Also, this was the time of pre-prohibition, and Dry groups (or supports of Temperance) argued that movies promoted drinking and other salacious activities.
Now if your question is about what influenced movies in the 1920's, a lot of movie ideas came from books, plays, and operas.