The significance of Light Yagami's rivalry with L in the anime "Death Note" is that it serves as a central and compelling plot point that drives the narrative forward. The clash between Light, who uses the Death Note to enact his own sense of justice, and L, a brilliant and enigmatic detective, creates tension, suspense, and complexity in the story. Their intellectual battle showcases themes of morality, justice, power, and the consequences of one's actions. Overall, the rivalry between Light Yagami and L is essential in shaping the characters and the overall direction of the series.