What does the following example illustrate? joy . . warm as the joy that children feel when they see their father's life dawn again, one who's lain on a sickbed racked with torment, wasting away, slowly, under some angry power's onslaught— then what joy when the gods deliver him from his pains! (5, 436-440)

This is a simile - a figure of speech that compares one thing to another. Homer compares Odysseus' joy to the children's joy when they see that their father has survived a grave illness. Odysseus has just survived a great danger because of Poseidon's anger. Athena has saved his life, and now he is happy and grateful. The simile draws a parallel between illness and storm at sea. Both are caused by angry gods, and only gods can save the day. Both are enlightened by the feeling of family's warmth and love, as Odysseus also has a family that is worried about his wellbeing, and is eagerly waiting for him to come home.