The rivalry between Light Yagami and L in the anime "Death Note" is significant as it serves as the central conflict of the series. Their intellectual battle and cat-and-mouse chase drive the plot forward and create tension throughout the story. The rivalry also highlights the themes of justice, morality, and the nature of good and evil as both characters have contrasting ideologies and methods in their pursuit of justice. Ultimately, the dynamic between Light and L adds depth to the narrative and keeps viewers engaged as they witness the psychological warfare between the two brilliant minds.