I think that the star system was an integral part of early Hollywood and the studio system. It is important because it essentially created American icons that reached a level of nationwide popularity previously unheard of. It was the concurrent creation of films with the popularization of radio that created the modern idea of “celebrity”. Audiences wanted to know about the actors and would go see a movie just because they were starring in it. The star system was the collection of particular actors or actresses by studios that would generate an audience. Some actresses and actors were “discovered” when they were young and trained to become audience favorites through a combination of singing, dance, and acting.
The star system affected what kinds of films the studio made because the films were written in order to reflect the talents of the actors. They had to showcase their particular talents. For instance, dance numbers for Fred Astaire, singing parts for Judy Garland, or diva roles for Mae West. Eventually, the star system caused the actors to gain power and ask for higher salaries.
For example, actress Dorothy Lee signed with RKO Pictures at the age of 18. She was type cast as a comedian and was made up to six movies a year at the peak of her career. The advertisements for the films always featured Dorothy Lee prominently, so that audiences would be attracted to the film. The star system was influential because it caused films in early Hollywood to prominently showcase the same talent over and over again, creating an American sensation of Hollywood Stars. (Imdb)
(on major film posters, the actor's names would be featured first and most prominently to advertise the star power)
Dorothy Lee, 1929.