An epithet is a word (usually an adjective) that is used to describe or characterize a specific attribute of a person or thing. It is often considered to be an abusive or disparaging description (such as a racial epithet), although there are several allowable definitions for the term. It should positively express an imaginative and accurate view of the subject. An example is given below from Homer's The Iliad:
Zeus-loved Achilles, you bid me explain
The wrath of far-smiting Apollo.
"Zeus-loved" describes Achilles, and "far-smiting" refers to Apollo.
As far as creating an epithet of your own, you might want to choose a character from The Odyssey, such as the Cyclops, and concentrate on creating an original descriptive term for it.