The significance of Light Yagami's rivalry with Near in the anime "Death Note" is that it represents the clash between two brilliant and strategic minds. Light, who aims to become the god-like figure Kira by using the Death Note to rid the world of criminals, faces off against Near, a prodigious detective who is determined to catch Kira and bring him to justice. Their rivalry highlights themes of morality, justice, and the consequences of power, as they engage in a psychological battle of wits to outsmart each other. Ultimately, their conflict serves as a key driving force in the plot and leads to a dramatic and intense conclusion in the series.