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Epicenter: the area directly above the focus of an earthquake.
Why do we need an epicenter?
Epicenters can be used to determine the location of an earthquake. Triangulation, the process of determining something's location using the locations of other things.
Earthquakes give off three kinds of waves. One kind, P-wave, is always faster than the others, S-waves and surface waves. The longer the distance the waves travel, the further ahead the faster wave gets. If a place feels both kinds of Earthquake waves, it can figure out how far away the focus of the Earthquake was.
Usually by determining the epicenter of three earthquake points, a circle is drawn around each of those points, its radius relative to the distance which the waves traveled. The point where each of the circles overlap is about the place where an earthquake will occur.
This is how the epicenter of an earthquake can be used.