Epigenetic is a term that describes changes in the way a plant looks (phenotype) without a mutation that changes the genetics of the plants. One of the best examples of epigenetics is the change in appearance in English ivy (Hedera helix) as it goes through the change from a juvenile to mature phase.
The juvenile phase is a vine with a lobed leaf. The mature phase can flower and the leaf is not lobed. Although the different phase look different, there is no change in the plant's genetics.
One of the important implications of epigenetics or phase change is the differences in the ability for cuttings to root from the juvenile versus the mature phase in woody plants.
In general, cuttings root most easily from juvenile phase cuttings. For more information see the section on juvenility.