How does Jiraiya die?

Jiraiya travels to Amegakure (Village Hidden in Rain) to investigate Pain — the leader of Akatsuki — and discovers that Pain is Nagato, his former student. He fights all six Paths of Pain simultaneously, loses his left arm, has his throat crushed, and is impaled by multiple black rods. He sinks into the ocean.

What makes his death so devastating?

Three things. First: he came back for his student. He could have sent subordinates; he went himself because Nagato was his responsibility. Second: he realizes as he's dying that Naruto's development as a person — exactly what he hoped to create — is the meaning of his life's work, not his victories. Third: his final act is encoding his message to Naruto in a toad's back. He cannot be stopped from communicating. He dies still writing.

What is the message he encodes?

The numbers correspond to letters in his published novel — a cipher that tells Naruto "the real one's not among them" (revealing that Pain's bodies are controlled remotely). Even dying, he's thinking tactically about how to protect his student.

How does Naruto respond to Jiraiya's death?

The Sage Mode training arc. Naruto processes grief through work — which is exactly what Jiraiya modeled. He doesn't stop; he builds. The entire Pain arc afterward is Naruto completing what Jiraiya started.

What does Jiraiya's death teach about mentorship?

That the mentor's greatest contribution is what the student does after the mentor is gone. Jiraiya's impact is measured in Naruto's response to the world without him — and Naruto's response is everything Jiraiya taught. The mentor lives in what he made. That's both sad and exactly right.