In a star with mass several times larger than the Sun's, fusion in the core continues until iron is created.  Now it turns out that fusion of iron (or any heavier element) does not produce energy - in fact it would require it.  So the core cannot support itself, and collapses.  In these massive stars, the core mass is greater than 1.5 solar masses.  Why is this a special number? In this case even the repulsive force of the electrons is not enough to support the core. The collapse continues to such a dense state that the electrons and protons in the core gas combine to form neutrons. Again, a density is reached when the repulsive force of the neutrons is sufficient to stop the collapse of the stellar core. At this point, the stellar remnant becomes stable and a Neutron Star is born. When it does so, it rebounds outward slightly, but the energy in this rebound is enough to completely expel the surrounding envelope at enormous speeds - the result is a Supernova Explosion. The remnant neutron star, barely the size of Albuquerque and containing a couple of solar masses of material, is much denser than even a white dwarf. A teaspoon of the neutron star material would weigh thousands of tons on Earth.

The picture below was taken with the Chandra X-Ray Telescope. It shows a naked neutron star inside the supernova remnant Puppis A. The remnant represents the outer layers of the star blown off in the supernova explosion while the neutron star is the collapsed core.