The story that made Eris famous outside the two early poems does not survive complete in either of them. It is known mainly through later summaries and allusions, tracing back to the lost epic the Cypria, part of the wider Trojan War cycle: every god and goddess was invited to the wedding of the mortal Peleus and the sea nymph Thetis except Eris, deliberately left off the guest list because her presence at any gathering was expected to end badly. She came anyway and threw a golden apple among the assembled goddesses inscribed simply "for the fairest," a single small object designed to produce exactly the argument it did. Hera, Athena and Aphrodite each claimed the apple, and rather than settle the dispute themselves the gods handed the choice to a mortal, the Trojan prince Paris, who judged Aphrodite the fairest after she promised him the most beautiful woman in the world, Helen of Sparta. That judgment, and the abduction of Helen that followed it, is the mythic spark later tradition gives for the Trojan War itself.
The episode is often read as Eris doing exactly what her name says without lifting a weapon: she does not fight the war, she only supplies the occasion for a rivalry that others carry to its conclusion, which fits both the Homeric Eris who spreads strife among people already inclined to conflict and Hesiod's bad Eris who delights in quarrel for nothing but itself. The Iliad itself never narrates the apple story directly, which is part of why scholars treat it as belonging to the wider Cycle tradition growing up around Homer's poems rather than to Homer's own text, but later Greek and Roman writers took the connection between Eris, the apple and the war's origin as settled background, and it is in that later, fuller form that the story is now best known.