Epigenetics refers to changes in your phenotype, including what you see (e.g., hair color) as well as what you do not (e.g., how much of a hormone is expressed), that do not correlate to changes in the DNA sequence. Most people are familiar with genetics, especially with all the new kits out there (like 23 and me) to find out your ancestry and learn about genes that might have implications for your health.
For example, if you find out that you have a version of a gene (called alleles) that has been correlated to a disease, that does not always mean that you will definitely get this disease. It might depend on what other factors you have been exposed to during your life, such as smoking or eating junk food all the time. This is just one of the many ways in which epigenetics might be important to understand why, among people sharing the same allele, some suffer diseases while others do not.