Secondary characters are supporting characters that help move the story along through their relationships with the main character. In Rick Riordan's Percy Jackson and the Olympians: The Lightning Thief, these secondary characters are mainly Annabeth Chase and Grover Underwood.
When Percy meets Annabeth, she comes across as stuck up and proud. She doesn't like Percy very much, and she could be described as being a little jealous of him. As the story progresses, Annabeth and Percy become close friends through the experience of going on a quest together. Annabeth also changes with Percy's help. At the beginning of the story, Annabeth does not have a good relationship with her father. Percy advises her to keep in touch with her dad, and by the end of the story, she has decided to go and live with him.
For Grover, he starts out as Percy's best friend that he met at the school he goes to, Yancy Academy. He is described as an outsider at school like Percy which gives them something in common. When Percy finds out he is a demigod, it is revealed that Grover was his keeper and a satyr. Keepers find campers and bring them back to Camp Half-Blood safely. Grover failed doing this with Thalia, Zeus' daughter, and it was ruled that he also failed to bring Percy to camp safely. Grover has to now prove himself by bringing Percy and Annabeth back from their quest safely. He succeeds at this.
Both of these characters not only change and develop in The Lightning Thief, but also through out the rest of the series as well. Although they are only secondary characters, they are essential to the whole story.