That point on the Earth's surface directly above the hypocenter of an earthquake. (USGS National Earthquake Information Center, 1999)
The location on the surface of the Earth directly above the focus, or place where an earthquake originates. An earthquake caused by a fault that offsets features on the Earth's surface may have an epicenter that does not lie on the trace of that fault on the surface. This occurs if the fault plane is not vertical and the earthquake occurs below the Earth's surface. (Noson, et.al., 1988)

This definition is in context to Earthquake. See more contextual defintions for Epicenter.