Figurative language is patterns of words which create images in the reader's mind, and also mean more than what they literally mean. There are many, many types of figurative language, but some of the most-often used ones are metaphor, simile, imagery, personification, hyperbole, and the sound-related figurative language (such as assonance, alliteration, onomatopoeia, etc.)
In the last book of the Odyssey, a simile presents itself almost immediately:
As bats fly squealing in the hollow of some great cave, when one of them has fallen out of the cluster in which they hang, even so did the ghosts whine and squeal as Hermes the healer of sorrow led them down into the dark abode of death. (Chapter XXIV)
We may not think of the squealing and scuttering of bats as a simile for ghosts anymore, since it has been used so often since Homer, but this simile creates a very clear and vivid image in the readers' minds of the sound and movement of the ghosts of the suitors in Hades.
Another example of figurative language is the rather mild one used by Odysseus to Laertes, when he is describing the sun on the vines Laertes gave him.
you also said you would give me fifty rows of vines; there was corn planted between each row, and they yield grapes of every kind when the heat of heaven has been laid heavy upon them. (Chapter XXIV)
This statement implies a personification (of the sun, which Homer and his listeners may have actually thought as a real being, the god Helios) that would "lay" the heat of the sun on plants, rather than the rays reaching the ground on their own. Another nice bit of imagery comes when the townspeople of Ithaca are talking about Odysseus killing all the suitors. "On this pale fear laid hold of them,". (Chapter XXIV). Fear cannot be seen, so we cannot know that it is pale. Faces are pale if they are fearful, the poet is saying, and thus shortens it and calls it "pale fear". This trope is repeated again near the end of the book.
Another simile ends the book. "But Odysseus gave a great cry, and gathering himself together swooped down like a soaring eagle." The use of fierce animals in similes for warriors is used often in Homer's poetry.