In Jonathan Livingston Seagull, the title character, Jonathan, is a seagull who finds himself bored and frustrated with the short-sighted, materialistic attitudes of the rest of his seagull flock. The other seagulls are only interested in fighting over food, but Jonathan wants to fly.
After he's kicked out of the flock, Jonathan trains for a while by himself. Eventually he learns to fly so high that he reaches another plane of existence—a sort of seagull heaven.
In this place, he meets Sullivan. Sullivan serves as a mentor to Jonathan, teaching him new flying techniques. Jonathan also meets the Elder Gull of this flock, a seagull named Chiang, who teaches Jonathan even greater secrets of flying. Sullivan calls Jonathan the best pupil he has ever had, and eventually Jonathan surpasses Sullivan's teachings and learns how to teleport.
When Jonathan returns to earth, he meets a seagull named Fletcher Lynd Seagull, who has been cast out by the flock for the same reasons Jonathan was. Jonathan starts to teach Fletcher how to fly better as well. In doing so, Jonathan begins to implement not only the lessons he learned from Sullivan on how to fly but also what he learned about being a good teacher.
Sullivan thus serves as a transitional character or a helper for Jonathan, the main character. Through Sullivan's influence, Jonathan grows from being a student to a teacher, from someone who flies "just because" to someone who understands the deeper aspects and techniques of flying. In this way, Sullivan is similar to characters like Obi-Wan Kenobi in Star Wars or Haymitch in The Hunger Games: he's someone the main character learns from so that, eventually, the main character can surpass their teachings.