Symbolism, Imagery, Allegory
When and how characters eat is extremely important to the symbolic texture of the Iliad. As you may have noticed, eating is a major social occasion for the Achaian warriors (this is maybe not so surprising). There are certain important rules of hospitality that govern eating. For example, when Odysseus, Phoinix, and Aias come to Achilleus's hut, as a sign of hospitality, he first cooks and serves them food and then asks them what their business is.
In light of this, it becomes extremely important when, after Patroklos's death, Achilleus refuses to eat breakfast with the other warriors, but instead wants to get to the battle as quickly as possible. On the one hand, this represents his alienation from the other warriors; on the other hand, some scholars have interpreted it as him symbolically acting in solidarity with his dead friend, who, naturally, cannot eat.
The symbolism of eating remains prominent during Achilleus's murderous rampage against the Trojans. When he tells Hektor that he wishes he were angry enough to "hack [his] meat away and eat it raw," this symbolizes his loss of humanity. (Cannibalism is generally considered anti-social.) Conversely, when Achilleus rejoins humanity through his connection with Priam, this moment is emphasized by the meal they share together – along with the speech Achilleus makes about the necessity of eating, even when one is in grief.