Earthquakes are violent, sudden disturbances that generate seismic waves, waves travelling outward from the origin of the earthquake in all directions. When describing an earthquake and its location, geologists often talk about its epicentre and its focus. The epicentre is located above the focus, but the two are different and, depending on the type of earthquake, may be separated by a large or small distance.
The focus of an earthquake is the point where the fault ruptures to cause the earthquake. In a sense it could be considered the "ground zero" of the earthquake, the point where the rock first shifts to make the earthquake happen. Seismic waves spread outward from the focus in all directions. As these seismic waves travel along or reach the earth's surface, they cause the shaking that you feel. The faster p-waves arrive first, but the slower surface waves that arrive shortly thereafter actually cause more damage.
The focus is underground and along the fault line. The point on the earth's surface directly above the focus is called the epicentre. Since the epicentre is closer to the focus than any other point on the surface, it experiences the most shaking and typically, though not always, the most damage. Earthquakes may be shallow-focus, in which case the focus is fairly close to the earth's surface, or deep-focus, in which case the focus lies buried deep below.
Shallow-focus earthquakes are by far the most common and release more energy, although deep-focus earthquakes in subduction zones can sometimes be huge. The most dangerous situation involves a quake, the epicentre of which lies beneath the ocean. If the quake is large enough, the disturbance to the seafloor can generate a huge wave called a tsunami. Tsunamis travel very rapidly -- as fast as 470 miles an hour -- and can cause significant damage far from the epicentre of the quake.
There are two types of plate boundaries where the focus of an earthquake might be found: convergent and transform plate boundaries. At the former, two plates are colliding head-on. If crust on one of the plates is oceanic, subduction may occur, and deep-focus earthquakes usually occur at these kinds of boundaries. Transform boundaries, like the one that runs through California, occur where two plates slide past each other. Earthquakes here usually have a more shallow focus.