One of the greatest events in Greek mythology was the Trojan War.  The Greeks believed that the war had taken place shortly after 1200 BC and had lasted for 10 years.  The Trojans were a non-Greek people living in the city of Troy (in what's now northwestern Turkey).  The cause of the war was Helen.  She was the wife of a Greek king named Menelaus, but she ran off with another man—a Trojan prince named Paris.  The Greeks demanded that the Trojans return Helen, and when the Trojans refused to do so, the Greeks declared war on them.  The entire war took place on battlefields right outside of Troy.  The war went back and forth, but after 10 years the Greeks were able to get inside the city.  They killed the Trojan men and enslaved the Trojan women and burnt the city down.

Seneca's play takes place right after the end of the war.  Here is a little more information on some of the characters how appear in the play:

Hecuba:  Hecuba is the wife of Priam, the king  of Troy.  Her husband was killed at the end of the war.  She is an old woman.

Andromache:  Andromache is the wife of Hector, the greatest fighter for the Trojans during the war.  Hector was killed by Achilles (the greatest Greek fighter) in the ninth year of the war.  Once he died, it was just a matter of time before the Greeks would win the war.

Astyanax:  Astyanax is the son of Hector and Andromache.  He is just a little boy.  The Greeks want him dead now because they hated his father so much.

Helen:  (see above)

Agamemnon:  Agamemnon is a Greek king who acted as commander in chief of the Greek forces at Troy.  He is the brother of Menelaus, the man whose wife, Helen, ran off with Paris to start the war.

Pyrrhus:  Pyrrhus is the son of Achilles, the greatest Greek fighter.  When Achilles was killed near the end of the war, Pyrrhus came from Greece and joined in the fighting.

Ulysses:  Known in Greek as Odysseus, he is an important Greek military leader.

Calchas:  Calchas is a seer (someone who knows the will of the gods and can tell people what lies ahead for them).  He is the official seer for the Greek side during the Trojan War.  Before they left Greece,Calchas told Agamemnon that they would win the war but that it would take a long time.
 

Much of the play revolves around what will happen to Astyanax and Polyxena now that the war is over and they have been captured.  The Greeks want Astyanax dead because he is the son of their great enemy Hector.  Polyxena is a daughter of Priam and Hecuba.  The ghost of Achilles has demanded that she be sacrificed to him (i.e. her throat would be slit and her body burnt in a religious ceremony, as if she were an animal; in reality, neither the Greeks nor the Romans practiced human sacrifice).