The difference between the folk understanding of epigenetics and the scientic understanding of epigenetics is the timescale. To scientists, epigenetics is the process by which genes become 'permanently' silenced via modifications to the DNA like methylation, or the histones the DNA is wrapped around. This kind of long term silencing is clearly important if you want to have a body made of different cell 'types' - a muscle cell should not make the same proteins as a neuron, so you'd want to shut the neuron genes off, forever, in a muscle cell, and shut the muscle genes off, forever, in a neuron. Now most of these long term marks are actually removed when making germ cells. Sperm and eggs, at some point, can shut off enzymes like DNMT1 that maintain these marks, so that the next person can start from a fresh slate...

Now the FOLK understand of epigenetics seems to have glommed on to an actually very small part of the actual phenomenon: there are a small set of genes that can be methylated in these germ cells, and the silencing will be passed on from parent to child so that the child will only express a certain gene from the mother or from father. This is called 'imprinting'. The folk understanding then extrapolates this, to genes being marked for several generations. I think evidence for this is poor, and not really the focus of most of the 'concept' of epigenetics. But there is still research to be done.