Who is Eteocles (from The Phoenician Women) from Euripides V and what is their importance?

Oedipus' son, Eteocles, and his brother, Polyneices, took control of Thebes after learning their father had married his mother and killed his father. They imprisoned Oedipus, who had gouged out his own eyes, in the palace. Oedipus cursed his sons to die by each other's swords.

Polyneices and Eteocles decided that in order to avoid conflict between the, the would take turns, year by year, ruling Thebes. Eteocles took the first turn, but when his rule was up, he refused to give up the throne. Power-hungry and ambitious, Eteocles valued his position above all else. He is bitter and resentful toward his brother for bringing an army to Thebes, and he will not even allow Polyneices to be buried in Thebes.

Eteocles offers to let Polyneices live in Thebes without power. He refuses. Thus, in order to avoid backing down, which he sees as cowardice, he decides to settle the battle once and for all by fighting his brother to the death. The brother fall victim to their father's curse by killing each other.