The Odyssey is considered to be an epic poem because it focuses on the adventures (and misadventures) of a single man, a hero who has both brains and brawn (though some epic heroes had more strength than intellect), and who travels far and wide on a particular quest (for Odysseus, it is to reach his home). The poem does begin, as epics do, with an invocation of the Muse:
Sing to me of the man, Muse, the man of twists and turns
driven time and again off course, once he had plundered
the hallowed heights of Troy. . . .
Launch out on his story. Muse, daughter of Zeus,
start from where you will—sing for our time too.
This is sort of like a prayer that the poet (or the person speaking the poem aloud) would use to call upon the Muse of epic poetry, named Calliope, in order to enlist her aid in telling the story well. Muses were associated with inspiration, so the speaker essentially asks to be inspired to do a good job, for the Muse to speak through him.
Epic poems are also characterized by the use of epithets, descriptive words or phrases that precede character names or place names in order to emphasize certain qualities; they can also help with the meter of the poem. Athena is often "grey-eyed" Athena; Penelope, Odysseus's wife, is often "heedful" Penelope; Telemachus, Odysseus's son, is often "princely" Telemachus or "heedful" Telemachus or even "cool-headed" Telemachus; Zeus is "Olympian" Zeus; the sea is the "wine-dark" sea, and so on.
Epic similes are another common feature of epic poems, and The Odyssey has a number of these. In the Cyclops's cave, Odysseus and his men prepare to blind the monster. He says,
So we seized our stake with its fiery tip
and bored it round and round in the giant's eye
. . . and the broiling eyeball burst—
its crackling roots blazed
as a blacksmith plunges a glowing ax or adze
in an ice-cold bath and the metal screeches steam
and its temper hardens—that's the iron's strength—
so the eye of the Cyclops sizzled round that stake!
Here, Odysseus compares the sizzling of the monster's one eyeball, when they plunge the fire-hot wooden stake into it, to a blacksmith plunging fire-hot iron into the water to cool it. Both evidently produce the same steam as well as the same "screech[ing]" sound (though, for the Cyclops, it's because he is screaming). These epic similes are rather grand comparisons that are so descriptive and detailed that they are quite easily visualized by the reader.