How did Jiraiya and Naruto's relationship begin?

Jiraiya was Naruto's godfather by arrangement — Minato and Kushina chose him, though Jiraiya was never told directly until much later. He first encountered Naruto in the original series during the Chunin Exams, took him on as a student during the Tsunade retrieval mission, and trained him for over two years before Shippuden begins.

What kind of teacher was Jiraiya?

Irreverent, inconsistent, and deeply effective. He taught Naruto Rasengan, Summoning Jutsu, and Sage Mode principles. He also disappeared to research and peep in hot springs. He was irresponsible in specific, documentable ways and completely reliable when it mattered. Naruto knew which was which — that was part of the lesson.

What did Jiraiya give Naruto that no one else could?

The sense that being imperfect, failing, and trying again anyway was the right approach. Minato was perfect. Kakashi was controlled and precise. Jiraiya was a mess — and kept going anyway, and wrote about hope, and believed in Naruto specifically when Naruto hadn't yet earned it. That belief is what Naruto says changed him.

What was their dynamic like?

Teasing, affectionate, mutually exasperated. Jiraiya called Naruto a brat. Naruto complained about Jiraiya's peeping. They bickered like family, which is what they were. When Naruto learned of Jiraiya's death, he asked to be alone and cried — and then came back and trained harder. Jiraiya would have understood.

What does their relationship model about godparenthood and mentorship?

That the best mentors are not role models in a perfect sense — they're people who model the imperfect persistence. Jiraiya showed Naruto that you can be a failure in many ways and still be worth something. That's more useful than excellence as a template.