Definition of "hero"

1) Modern

a) Anybody you admire.  E.g., a movie star.  "My hero."

b) Protagonist in a work of literature.  Leopold Bloom in Joyce's Ulysses.

c) Someone who acts bravely.  Police and firemen on 9/11/01.

2) Ancient Greek

a) Hero of cult.
Spirit or demon worshipped at his grave.  Power to harm or help.  Chthonic religion.

b) Hero of legend.

Warrior who fought at Troy or participated in any of the other great events of that period.  The term is partly just an acknowledgement of social standing and means something like "noble gentleman."  ("Heer" and "Sir" are cognates.)

c) Offspring of a mortal woman and a god.

May overlap with preceding.  Zeus has a son on the battlefield at Troy.