It can be argued historically that American Theater during the 1920's represented the new social,economic, and political American experience. Essentially American theater was just that American, prior to this decade theater was a European domain. However, American theater began before the 1920's at The New Theater at 62nd and Central Park West further uptown from the old Broadway was the precursor to the theater of the 1920's. Funded by New York's wealthy, Vanderbilt, Morgan, and others the theater offered tolerance of the new social attitudes that were emerging but the sound inside the theater was horrible. By 1920's the LaGallienne movement led by Eva LaGallienne sought to bring an intellectual, not for profit genre to the theater. Operating from a 14th Street theater this 'new' theater experience by 1926 depending upon the play included intellectualism, African American actors and controversial topics led by Mae West and sex. American theater during the 1920's was simply reflecting the shift already taking place within American society. The old European style of theater had lost its luster (WWI caused that fate) and American theater during the 1920's was a reflection of the new social structure that emerged during that 'roaring' decade, out with the old in with the new...American new.
The previous answer is really good, American serious theatre was breaking away from European traditions. But the most common theatrical presentations in America were not serious art, or musicals, but what was termed "vaudeville." These were short acts; musical, singers, comedy, one-act plays, dancers, jugglers, acrobats and animal acts. Most of he great comedians,singers and movie stars of the 1930s through the '60s had usually begun in vaudeville, which flourished from the late Victorian period through the 1920s. The Palace in Times Square was the top venue for vaudeville, eight acts a show, two shows a day. Although many of the performers enjoyed a social status just above vagrants, some were rich and famous, such as comedian Walter Kelly (Grace Kelly's uncle) and Scottish minstrel Sir Harry Lauder. Charlie Chaplin, the Marx Brothers, Mae West and all six of the "Three Stooges" came out of vaudeville. It may have been more low-brow than the legitimate theatre, but it was "respectable entertainment" for the masses, and the theatre that the vast majority of the populace saw. The rich, famous and powerful were often fans, too, such as Woodrow Wilson.