The prefix epi, or ep if followed by a vowel or the letter "h", is derived from the Greek preposition ἐπί meaning: above, on, over, nearby, upon; outer; besides, in addition to; among; attached to; or toward.Thus, when someone describes some phenomenon as being caused by "epi-*," it generally means "I am sure the cause is around * somewhere."
When someone tells you that something is "epigenetic," what they mean is, "I'm sure it's something to do with the genes, and while it isn't the genes themselves (or I'd say it was genetic, and be expected to prove I was right about that), I'm sure that the cause has got to be around the genetics somewhere."
Very often this is a completely unproven assumption. It strikes people as plausible because (a) we don't fully understand how genes work, but (b) we do know that various factors seem to 'turn on' or 'turn off' their functionalities. The implication is meant to be that some factor -- we don't know what or how -- is acting on the genes somehow. But in fact, we often can't really say that the genes have anything to do with it.
With all that said, read this article.