Eris is the Greek goddess of strife, and the daughter of Zeus and Hera.
History
The most famous tale of Eris recounts her initiating the Trojan War. The goddesses Hera, Athena, and Aphrodite had been invited along with the rest of Olympus to the forced wedding of Peleus and Thetis, who would become the parents of Achilles, but Eris had been snubbed because of her troublemaking inclinations.
She therefore tossed into the party the Apple of Discord, a golden apple inscribed Kallisti– "For the most beautiful one", or "To the Fairest One" – provoking the goddesses to begin quarreling about the appropriate recipient. The hapless Pairs, Prince of Troy, was appointed to 'select the most beautiful' by Zeus. Each of the three goddesses immediately attempted to bribe Paris to choose her. Hera offered political power; Athena promised skill in battle; and Aphrodite tempted him with the most beautiful woman in the world: Helen, wife of Menelaus of Sparta. While Greek culture placed a greater emphasis on prowess and power, Paris chose to award the apple to Aphrodite, thereby dooming his city, which was destroyed in the war that ensued.
The series
Eris doesn't appear in the series, but she was probably on Olympus when Percy, Annabeth, and Grover went there.
She is mentioned The Sea of Monsters, after recieving a call Hermes says to redirect the call to Eris at customer service.
Her apple trick is mimicked by the Stoll brothers on the Aphrodite cabin. They spray-painted an apple gold, wrote 'For the hottest' on it, and threw it in the cabin. This was regarded with amusement by the rest of the camp, as the demigod children of Aphrodite fought over the apple.