This is a good question. First, it is important to start off with a definition of a metaphor.
A metaphor is a literary device where a word or phrase is used to describe something to which it is not literally applicable. An example of this would be the great hymn of the Protestant Reformer, Martin Luther, when he penned, "A mighty fortress is our God."
When we come to Homer, it is important to say that he does use metaphors as much as he uses similes. An example of a metaphor in the Odyssey, is when Homer writes, "Nine years we wove a web of disaster." Another example is when Homer says: "[Odysseus is] fated to escape his noose of pain".
Homer actually uses a literary device that is unique to his type of work. In fact, it's even named after him--the "Homeric simile." This is a special kind of metaphor used in epic poetry. (It's also called the "epic simile.")
The Homeric simile is a really detailed comparison that is many lines long. It usually makes a comparison to some natural thing/animal in the midst of some kind of event. One of the most common ones used in Homer's works is a long passage comparing a fighting warrior to a specific wild animal (like a lion or a wolf). They often occur in moments of intense action or emotion.
It's important to remember that Homer's works, like the Odyssey, were originally oral poems. They were recited out loud and by memory. That means that they needed to include a lot of literary elements that made it easier to memorize the poems. Homeric similes are a great example of this. Not only do they capture the audience's attention, but they allow the reciter of the poem to have something easy to alter in the middle of the poem.