The film is composed of five episodes:
- "Men and Maggots" (Люди и черви), in which the sailors protest at having to eat rotten meat;
- "Drama on the Deck" (Драма на тендре), in which the sailors mutiny and their leader, Vakulinchuk, is killed;
- "A Dead Man Calls for Justice" (Мёртвый взывает) in which Vakulinchuk's body is mourned over by the people of Odessa;
- "The Odessa Steps" (Одесская лестница), in which imperial soldiers massacre the Odessans.
- "One against all" (Встреча с эскадрой), in which the squadron tasked with intercepting the Potemkin instead declines to engage; lowering their guns, its sailors cheer on the rebellious battleship and join the mutiny.
Eisenstein wrote the film as a revolutionary propaganda film, but also used it to test his theories of montage. The revolutionary Soviet filmmakers of the Kuleshov school of filmmaking were experimenting with the effect of film editing on audiences, and Eisenstein attempted to edit the film in such a way as to produce the greatest emotional response, so that the viewer would feel sympathy for the rebellious sailors of the Battleship Potemkin and hatred for their overlords. In the manner of most propaganda, the characterization is simple, so that the audience could clearly see with whom they should sympathize.
Eisenstein's experiment was a mixed success; he "was disappointed when Potemkin failed to attract masses of viewers", but the film was also released in a number of international venues, where audiences responded positively. In both the Soviet Union and overseas, the film shocked audiences, but not so much for its political statements as for its use of violence, which was considered graphic by the standards of the time. The film's potential to influence political thought through emotional response was noted by Nazi propaganda minister Joseph Goebbels, who called Potemkin "a marvelous film without equal in the cinema ... anyone who had no firm political conviction could become a Bolshevik after seeing the film". He even was interested in getting Germans to make a similar film. Eisenstein did not like the idea and wrote an indignant letter to Goebbels in which he stated that National Socialistic realism did not have either truth nor realism. The film was not banned in Nazi Germany, although Himmler issued a directive prohibiting SS members from attending screenings, as he deemed the movie inappropriate for the troops. The film was eventually banned in some countries, including being banned at various times in both the United States and France, as well as in its native Soviet Union. The film was banned in the United Kingdom longer than any other film in British history.