Why do you think Percy asks Chiron about the underworld? He says "the beginning's of an idea—a tiny, hopeful fire—started forming in my mind." What does he mean?

On the way to Camp Half-Blood, the Minotaur attacks their car. Grover is knocked unconscious, so Sally and Percy carry him up the hill. Sally is unable to cross camp borders, and so the Minotaur catches her. She disappears in a flash. Although Percy is able to defeat the Minotaur with its own horn, his mother is still gone.
At camp, Percy is still adjusting to the new information that Greek myths are real, but the idea of the underworld intrigues him and gives him hope. The Minotaur is from the underworld, so if it is a real place, then perhaps his mother is not really dead. If one can travel to the underworld, then perhaps Percy can go there to rescue his mother and bring her back.
This quote shows how Percy starts to form an idea that will carry him through the rest of the story.