In the first book of Homer's Iliad, we encounter a dispute over a war prize between Agamemnon and Achilles, culminating in Achilles withdrawing from the fight between the Greeks and Trojans, mainly to sulk in his tent. The plot of the Iliad focuses on the "wrath of Achilles" and the way in which it weakens the Greek side in the war.
Achilles is the greatest warrior of the Greeks, in part because he has been made invulnerable (except for his heel) by his mother. He has great physical strength and skill in battle. On the other hand, despite being an outstanding fighter, he is leader only of the Myrmidons, from Thessaly, not the overall leader of the Greek army, and thus lacks the authority to make strategic decisions.
Agamemnon is the king of Mycenae, the wealthiest and most powerful city in Greece of this period, and is the leader of the Greek forces. Although he is not as strong a warrior as Achilles, he has authority and legitimacy as a leader.