"Epi-Graph," as in "Epi-Dermis"

• "Epi" means "on top of," as in "epidermis."
• "Graph" means "writing."
• An epigraph, then, is "on top of the writing."
  
• The epigraph follows the title, and, like the title, its job is informational and supportive. ("Newspaper misprint for 'mammoth'.") The epigraph and its source, if it has one, and it usually does:
  

What do women want? -Sigmund Freud

should be set off in italic type. An epigraph should never be:

• longer than the poem
• better than the poem
• unnecessary
• unintelligible
  

In your entire body of work you should not have more than three or or four works topped with epigraphs. Epigraphs include dedications. ("To my student, thrown by a horse.") Epigraphs and dedications are extraneous to the works, and therefore they are weaknesses. If you have something to say, say it in the work, not in the toppings.

An epiGRAM (meaning "on top of the MESSAGE") is a short, highly crafted, pointed statement, a "quotable quote," a summary or generalization about just one topic: "Tis with our judgements as with our watches: None go just alike, yet each believes his own." -Alexander Pope.

Pope's epigram might make a good epigraph. But it's better not to rely on somebody else's work to bolster yours.