In the Iliad's first book, the conflict between Agamemnon and Achilles (and the result of that conflict) has tremendous implications over the course of the war.
The poem opens after Agamemnon has taken Chryseis (the daughter of Chryses, a priest of Apollo) as a war captive, with her father offering a ransom for Chryseis's return. When Agamemnon refuses to accept said ransom, he angers Apollo (which results in no small suffering for the Greek forces). Ultimately, it is determined that Agamemnon must release Chryseis to satisfy Apollo, but Agamemnon demands that, if he is to release Chryseis, he must be compensated with another man's captive. When this brings him into conflict with Achilles, Agamemnon determines to take Achilles's own captive, Bryseis. This rift between Achilles and Agamemnon has critical implications for the remainder of the poem.
Outraged, Achilles responds by removing himself from the war, while also appealing to his mother (the nymph, Thetis). Thetis herself appeals to Zeus, asking him to support Troy to punish this slight against her son. In this way, Achilles's complaint against Agamemnon actually has a cosmic dimension to it as well, through Thetis and her intervention with Zeus, most powerful of the gods.
At the same time, remember that Achilles is the greatest warrior among Agamemnon's forces. From that perspective, his removal from battle represents a significant loss to the Greeks, while the war is still ongoing. Recognizing this, the Greeks will later try to pacify Achilles, but it is not until the death of his friend...
Patroclus at the hands of Hector that Achilles, enraged, returns to the battlefield.