The cat-and-mouse game between L and Light Yagami in the anime "Death Note" is significant because it serves as the central conflict of the series. It showcases the intellectual battle between two genius characters with opposing ideologies—one being the brilliant detective L, who is determined to catch the mysterious serial killer Kira (Light Yagami), and the other being Light Yagami, who is using the Death Note to eliminate criminals in the name of justice. This game of wits creates suspense, intrigue, and psychological tension throughout the series, making it a thrilling and captivating watch for viewers.