The hypocenter (literally: 'below the center' from the ancient Greek υπόκεντρον) refers to the site of an earthquake or a nuclear explosion. In the former, it is a synonym of the focus; in the latter, of ground zero.
An earthquake's hypocenter is the position where the strain energy stored in the rock is first released, marking the point where the fault begins to rupture. This occurs at the focal depth below the epicenter.
The focal depth can be calculated from measurements based on seismic wave phenomena. As with all wave phenomena in physics, there is uncertainty in such measurements that grows with the wavelength so the focal depth of the source of these long-wavelength (low frequency) waves is difficult to determine exactly. Very strong earthquakes radiate a large fraction of their released energy in seismic waves with very long wavelengths and therefore a stronger earthquake involves the release of energy from a larger mass of rock.
The term hypocenter also refers to the point on the Earth's surface directly below an atmospheric explosion. In principle, it applies to any such explosion but the term was not found to be necessary until the advent of massive nuclear explosions. In this context, the term 'ground zero' was synonymous with hypocenter, though the ground zero term is less precise, as it has been used ever more loosely.