In the first book of Homer's Iliad, it is difficult for a modern audience to recognize heroism, mainly because few of the characters do anything that seems heroic from a modern perspective. Agamemnon seems like a bully and Achilles seems like a whiney baby. If we read carefully, however, we can pick out various bits and pieces that provide a Homeric definition for heroism.
One defining characteristic of the Homeric hero is that he accomplishes great things on the battlefield. The most heroic characters are the ones who gain honor by helping defeat the enemy and who acquire plunder from the enemy. Achilles hints at this in his complaint about Agamemnon:
When the Achaeans sack some rich Trojan city, it’s not I who win the prize. My hands bear the brunt of the fiercest fight, but when the wealth is shared, yours is the greater, while I return, weary with battle, to the ships, with some small fraction for my own.
Another aspect of Homeric heroism is excellence in speech. King Nestor of Pylos describes this concept well when he tries to advise Agamemnon and Achilles. Note also his emphasis on the military prowess as well:
They summoned me, and I joined them, travelling far from Pylos. I held my own among them, though against them no man on earth could fight. Yet they listened to my words, and followed my advice. You too should do the same, for that is wise.
Thus, even though most of the major characters in Iliad I do not appear very heroic from a modern perspective, if we read closely we can find that prowess in words and deeds is a hallmark of the Homeric hero.