It is well worth understanding the context of the play in terms of family tree, and the myths that go along with it. The family relationships in this play (and, indeed, in the other versions of the same myth) are illustrated on this simplified family tree (though note - significantly - that Sophocles adds two other strands which are not depicted here: that Clytemnestra marries Aegisthus after Agamemnon's death, and that Agamemnon and Clytemnestra have another daughter, Chrysothemis).
Here are simplified versions of the key myths up to the start of the play - which explains why the Chorus might be right to address a curse on the House of Atreus.
Tantalus
Tantalus decided to cook his own son Pelops, and feed him to the gods at a banquet. This was to find out whether the gods really were omniscient - would they know that they were eating human flesh? Most of them did know, but Persephone, who was distracted, ate some of Pelops' shoulder.
Tantalus' punishment for committing this crime was to be sent into the underworld, where he stands for eternity up to his chin in a pool of water. Every time he tries to drink, the pool drains before he can touch a drop. Above him are low hanging fruit, which lift out of reach when he tries to grab it. From his name, we derive our word "tantalize".
The gods brought Pelops back to life, replacing his shoulder with ivory. The family, though, were cursed ever afterwards.
Pelops
Pelops sabotaged the chariot of his would-be father in law, so that he could marry Hippodamia. He then killed Myrtilus, who cursed Pelops as he died.
Atreus & Thyestes
Atreus and Thyestes murdered their stepbrother Chrysippus.
Atreus then vowed to sacrifice his best lamb to Artemis, but, when he found a golden lamb, he gave it to his wife to hide from Artmies. She in turn gave it to her love, Thyestes (Atreus' brother!) who managed to convince Atreus that whoever had the lamb could be king. Atreus agreed, and Thyestes produced the lamb and took the throne. Atreus performed a similar trick on Thyestes and regained the throne, banishing Thyestes.
Atreus then, however, learned that Thyestes had slept with his wife. He took Thyestes' sons, killed them and cooked them, saving their hands and feet. Thyestes then ate his own sons, without knowing it, and was taunted by Atreus with their hands and feet.
An oracle told Thyestes to father a child on his daughter, Pelopia, who would then murder Atreus for him. Aegisthus, that child, was abandoned by his mother, found, and given to Atreus who raised him as a son. When Aegisthus was told of his true father and grandfather (both Thyestes!) he killed Atreus.
Agamemnon
One of Atreus' two sons, Agamemnon married Clytemnestra. Agamemnon killed a sacred stag in the goddess Artemis' sanctuary. The prophet Calchas told Agamemnon that, to appease the goddess, and to get winds to sail ships to Troy, he would have to sacrifice his daughter Iphigenia.
He did sacrifice Iphigenia, and Agamemnon went to Troy in a warship. On his return, Clytemnestra avenged her daughter's sacrifice by killing Agamemnon.
