Arete is honor and excellence. Males achieved arete in the Ancient Greek world by becoming valiant warriors. War was the chief source of male honor in life and after death, for courageous fighters were revered and remembered.
Yet, as Homer shows, the arete wrested from warfare also leads to sadness and death. Men show their valor in the Trojan War, but they also participate in a long and bitter bloodbath.
Achilles is one example of the doubled-edged sword of arete. He is offered a choice: a long and peaceful life, or a short life of arete through being a great warrior. He chooses the latter, as this is what his culture most reveres. Achilles does achieve glory and is remembered after death, but his short life is fraught with grief, such as when Patroclus is killed in battle while wearing his armor. Achilles's fame and honor come at a high price.
Hector would prefer to stay at home with his beloved wife and young son, living in domestic bliss, but he feels bound to fight. A life turned away from doing his duty as soldier would be a life of such dishonor he can't contemplate it, much as he desires it. He does his duty and fights valiantly, but the cost of his arete for him—and his wife and son—is very high indeed.
War brings arete, but it also brings anguish: Homer raises the question in both the Iliad and the Odyssey of whether the glory is worth the price.
For the purposes of this discussion, I'm going to translate arete as "excellence." There are many ways that this can be achieved, but the most highly prized is through feats of great physical courage on the battlefield, of which there are numerous examples in The Iliad. Excellence in friendship must also be mentioned, not least because it's Achilles's close bond with Patroclus that causes him to emerge from his tent after his lengthy sulk and return to the fray. For Achilles, both forms of excellence are closely linked.
Patriotism is another form of excellence, one in which Hector excels over Achilles. Hector always fights for a higher cause, for the honor of his family and his city. Troy is everything to him, and he'll do whatever it takes to protect it from the marauding Achaeans. Achilles, on the other hand, fights for his own personal glory. He's such an egomaniac that he's quite prepared to mope around his tent while his comrades are being slaughtered outside.
Women also show excellence in The Iliad. However, their opportunities for doing so are more heavily circumscribed, given the much more restricted role of women in ancient Greek society. Although women are generally restricted from displaying excellence in battle, they can still make sacrifices and offer sage advice to the men; this is another form of excellence. In book 6, Andromache tries to dissuade her husband, Hector, from returning to the murderous heat of battle, pleading with him to remain with his family. But Andromache's arete clashes directly with Hector's, and there can be no compromise between them. Hector knows that he must do his duty and go back out to fight, irrespective of the consequences.
The term arete can mean "skill" or "excellence" in Homeric Greek. Its etymological connection with "Ares" (the god of war) also conveys a sense of martial prowess. The sense of arete as an overarching and specifically moral virtue that we see in Plato is actually rather specific to Platonic and later philosophical thought. This very abstract sense of Platonic arete differed from that in Homeric Greek.
The importance of "arete" is connected to two other key concepts in Homer: "kleos" (fame or reputation) and the notion of "aristeia" (supreme excellence, derived from "aristos" meaning "best"). With the afterlife being regarded as unimportant or even inferior in Greek religion, the goal of the aristocrats in Homer was to achieve undying "kleos," the sort of fame that would live forever in cultural memory, passed down by generations of poets and artists, bringing permanent glory to the aristocrat and his descendants. Arete, or excellence, would lead to being the best ("aristos") fighter on a given day and perhaps even to a moment of greatness, such as the battle between Achilles and Hector.
In a sense, the Trojan War was not just a competition between Greek and Trojan fighters but also a highly individualistic competition in which all of the individual participants were displaying their arete on the field of battle in order to be proclaimed the best (aristos) fighter and gain fame and glory (kleos).
Arete is the term given to excellence or honour that was won by heroes by achieving feats of great skill or bravery. Arete is a central theme to this book as the warriors all are striving to gain arete during the Trojan War and seek to show themselves as being more honourable and excellent than other soldiers.
Particularly interesting to this debate is the conflict between Achilles and Hector, and which gains more arete. You might want to consider yourself which of these two characters gains more arete than the other.
Certainly, Hector seems to be a stereotypical hero. He shows massive loyalty and bravery in the face of unfavourable odds and is self-sacrificing to the extreme. We can argue that he most definitely gained arete before his death. Achilles, on the contrary, does not show himself to be the same kind of hero. For a large proportion of this text he is absent from the battlefield, withdrawing his services because of what Agamemmnon did to him through the woman he won, Briseis. He spends more time throwing tantrums over the loss of his honour and ironically lessening his arete. Although in the end he is spurred into battle and defeats Hector, it is only to gain revenge that Achilles does this.
Thus which characters gain arete and how is a key question and theme that runs throughout this novel and helps us to consider how characters are compared and contrasted with each other.