The Executive Producer is an undefined title, often given to those (or representatives of those) who facilitate the production of the movie, either by financing it or alleviating other major problems. It can range from the person who initialized contact with the people who provides financing, or the person who wrote the book that the film is based on.
Rarely in the movie business does the writer or director put up his or her own money to create a film. Instead, they get one or more Executive Producers to supply their money in exchange for part of the profits earned by the movie.
In a studio setting, the Executive Producers are supervisors of the production team, and make sure that deadlines are met, and that budgets are kept. In an independent film setting, Executive Producers generally don't interfere with the making of the film, but they still expect you to make a decent (or better) movie.