Eris tempted Eri with a golden apple to possess and use her as a tool to start chaos in this world. As she caught Saori Kido (Athena), she placed a golden apple in front of Saori's chest to drain her power and life force to the point she would no longer need Eri's body, and proceeds with her plan to take over the world. Whereas it had been foretold that when Athena were to die, all of the dead Saints with grief in their hearts would be revived and finish Earth's destruction.

In Greek mythology, when Eris was not invited to the wedding of Peleus and Thetis due to her trouble-making nature, she tossed a golden apple on the ground in front of Hera, Athena and Aphrodite that inscribed "to the most beautiful goddess" which sparked a contest between the three goddess and eventually lead to Trojan War.

(Source: Wikipedia)