From the Metropolitan Opera website:
The opera is set in Crete, about 1200 BC. Helen, the wife of King Menelaus of Greece, has been carried off by Paris, son of King Priam of Troy, triggering the Trojan War. As she is also the sister-in-law of Agamemnon, several Greek kings allied with him have joined forces to lay siege to the city of Troy. One of these kings is Idomeneo (Idomeneus) of Crete. Having been away for many years, Idomeneo has, prior to his victorious return, sent ahead of him some Trojan captives, including Priam’s daughter, the princess Ilia. On her arrival in Crete she is rescued from a storm by Idomeneo’s young son, Idamante, who has ruled as regent in his father’s absence. The two have fallen in love. Princess Elettra, daughter of Agamemnon and Clytemnestra, also loves Idamante. After Elettra and her brother, Oreste, killed their mother and her lover, she was forced to flee their home in Argos and has taken refuge in Crete.