Eris is the Greek goddess of strife and discord. She has one child (with Zeus) whose name is Ate, goddess of Hate. Her Roman equivalent is Discordia.
In the Trojan War myth, Thetis and Peleus (Achilles' parents) had a wedding to which every Greek deity was invited - every deity except Eris. The furious goddess vowed revenge. She stole a golden apple from the Tree of the Hesperides (Zeus' wedding present to Hera) and carved the words "τῇ καλλίστῃ" (tei kalliste, meaning to/for the fairest/most beautiful) into it. A dispute between three claimants (Athena, Hera and Aphrodite) led to Zeus having to decide between them. Realising the precarious position he was in by having to choose between his wife and two daughters, Zeus sent Hermes to a shepherd named Paris, and asked him to judge.
Paris was not known as a Prince of Troy because a prophecy said he would bring destruction to Troy. The three goddesses offered Paris "gifts" if he would choose them; Hera offered him rulership of many lands, Athena offered him unlimited wisdom and Aphrodite offered him the most beautiful woman on the Earth.
Paris chose Aphrodite, who gave him Helen of Sparta as a gift (despite the fact she was married to Menelaus). Athena and Hera thus supported the Greeks in the Trojan War whilst Apollo, Zeus, Poseidon, Aphrodite, Hephaestus and Artemis supported Troy. During the sack of Troy, Eris was present with her sister/companion Enyo.