A neutron star is a star whose core is made up mostly of neutrons. They are what's left of stars that were four to eight times more massive than the sun. These stars originate from catastrophic explosions called supernovae.
The centers of these supernovae collapse to the point where the electrons and the protons in the atoms fuse into neutrons. This causes a star so dense that though it may be only 12 miles in diameter, it's still 1.4 times more massive than the sun and has gravitational and magnetic fields millions of times stronger than those found on Earth. Pulsars are rotating neutron stars.