In Homer's Iliad, the epic poet's heroes are often motivated by kleos, a Greek word which can carry meanings such "good reputation", "fame", and "glory." In the opening of Iliad 5, for example, goddess Athena inspires Diomedes so that "he’d stand out and win heroic glory [kleos]" (A.S. Kline translation). In Iliad 9, after Achilles withdraws from the fighting, we find him in his tent singing (ironically) of the glorious deeds of other warriors. Thus, for Homeric heroes such as Diomedes and Achilles, the achievement of glorious deeds is a significant motivation. Failure to achieve such deeds would make them rather ordinary men.
As for the concept of nostos, which means "return" or "return home," this is a theme dealt with more frequently in the Odyssey than the Iliad. The Odyssey focuses almost entirely on Odysseus' nostos. Still, nostos versus kleos is a choice that Achilles must face. At Iliad 9.413, Achilles must decide between going back to Greece and living to old age, or remaining at Troy and dying young, but gaining everlasting glory. Hector's onslaught against the Greek camp and his threatening to set fire to the Greeks' ships will take away Achilles' nostos (Iliad 16.82), so Patroclus begs Achilles to let him lead their troops into battle. When Achilles agrees and Patroclus goes into battle and is killed by Hector, this event seems to seal the fact that Achilles will not return home, but will stay at Troy, kill Hector, and gain everlasting kleos.