The Iliad finishes before Achilles is killed. Paris, the Prince of Troy, shoots a poisoned arrow that hits Achilles’ heel. But the epic poem concludes right after Hector’s honorable funeral. The events that entailed the fall of Troy are not part of The Iliad.
The central conflict in the text is the quarrel between Agamemnon and Achilles. The first lines of the poem mention the warrior’s rage, and all the text describes the consequences of his anger. In brief, Agamemnon took Achilles’ war prize, Briseis, because he had to return his own captive woman to her father. Achilles agreed but refused to contribute to the war anyhow. Many deaths had to happen until he changed his mind.
Patroclus, Achilles’ friend, was killed in action, and the hero wanted to revenge. He kills Hector (who is responsible for Patroclus’ death) and dishonors his body. Priam, Hector’s father, comes to the Achaean camp to collect his son’s corpse. Achilles agrees to his request, and they cry together for all the deaths that the war caused. King Priam holds Hector’s funeral. Here the poem finishes.
This summary shows that Achilles’ death is a part of another story beyond Homer’s purpose in The Iliad. He told us a moral lesson about the restoration of an insulted honor and how bloody this route may be.
As we know from other Greek myths, Apollo helps Paris to shoot Achilles in his heel. It is the only unprotected place on his body. It was a cowardly murder that tells a lot about Paris. Achilles dies on the spot, remaining to be the hero that was never defeated in battle.