Achilles was the most famous and powerful of the warriors named in Homeric tradition. His beauty was compared to that of the Gods, and in his infancy he was dipped into the river Styx and made invulnerable; only his heel, where his mother, the nymph Thetis gripped him, remained mortal.
The Iliad specifically does not cover the time of Achilles's death at the bow of Paris, and so the resurrection referred to was not one of his mortal body. Instead, the resurrection was a spiritual and mental one.
After the kidnapping of his slave/lover Briseis, Achilles declares that he will no longer fight. For him, this is a fate worse than death itself, for he has been told that he would die in the war and his name live forever. Furthermore, he has dedicated his entire life to battle; it is the entire reason for his existence. In his prayer to Thetis, he says:
"...you bore me doomed to live but for a little season; surely Jove, who thunders from Olympus, might have made that little glorious. It is not so. Agamemnon, son of Atreus, has done me dishonour, and has robbed me of my prize by force."
Without Achilles and his warriors, the battle turns against the Greeks. Achilles remains steadfast in his refusal to fight until Patroclus, clad in Achilles's armor, dies on the field. Achilles is driven mad with anger and strikes powerfully against the Trojans, "resurrecting" his honor, image, and purpose in life.
As a fire raging in some mountain glen after long drought- and the dense forest is in a blaze, while the wind carries great tongues of fire in every direction- even so furiously did Achilles rage, wielding his spear as though he were a god, and giving chase to those whom he would slay, till the dark earth ran with blood.