There is information available on eNotes on the term epithet. Directing you to that information will be much more concise than defining the term here, as it is a term with a number of meanings.
You can follow this link for a lengthy description of the term in its various meanings: http://www.enotes.com/topic/Epithet
Also, for future reference, you can do a search within eNotes to find pages and links to quite a bit of material on many subjects, including specific terms like this one.
When you do a search for epithet, a page/tab shows as a Wikipedia result. Clicking the tab takes you to an eNotes page with all the information you are looking for.