Put more simply epigenetic theory is "an emergent theory of development that emphasizes the interaction of genes and the environment - that is, both the genetic origins of behavior (within each person and within each species) and the direct, systematic influence that environmental forces have, over time, on genes."
Animal development is used as common examples to illustrate epigenetics. "For example, the shape of an animal's face and the color of its fur are the result of genetic factors, but some species develop abnormal facial features or change the color of their fur depending on environmental conditions. Even biological sex can be epigenetic: Experimenters incubated a clutch of alligator eggs at various temperatures. At about 32C all the baby alligators became male, and below that temperature all became female (Ferguson & Joanen, 1982)."
Quoted from Berger's The Developing Person.