Neutrons in isolation are unstable.  They will energetically decay, becoming a proton, electron, and an anti-electron-neutrino with a half-life of about 10 minutes.  This is called ß-decay.  

This reaction is reversible through a process known as electron capture.  If a proton and an electron are forced into near proximity, they can combine to form a neutron, emitting a normal electron-neutrino.

In the collapsing iron core of a high mass star, in the last microsecond before it blows itself to kingdom come as a type 2 supernova, the electrons and protons within the iron are forced together and undergo this inverse ß-decay becoming neutrons and emitting an overwhelming barrage of neutrinos.

The newly formed neutrons rapidly sort themselves out into energy shells.  Neutrons are fermions.  Identical fermions cannot co-exist together in the same system.  Thus the neutrons in the collapsed core separate into a vast number of different energy shells.  Low energy neutrons are deeper in, higher energy neutrons are farther out.  There is no way for the higher energy neutrons to lose energy since all the lower shells are full.  

All those neutrons are in a constant state of vibration and collision.  Higher energy neutrons vibrate and collide faster than lower energy neutrons.  All that vibration and collision creates an outward pressure that holds back the inward crush of gravity.  So the object, now only a few miles in diameter, settles into a stable state called degenerate matter. 

This object is often called a neutron star; and the degenerate matter within it is sometimes referred to as neutronium.  A teaspoon of neutronium would weigh several billion tons.  

Much of the angular momentum of the original star remains within the neutron star.  However, since the radius has shrunk by three or four orders of magnitude, the angular velocity has increased by a corresponding factor.  These objects can spin at thousands of RPM.  Moreover, much of the original star's magnetic field is trapped within the neutron star, and has likewise been compressed by several orders of magnitude.  Thus, the neutron star is a very powerful spinning magnet.

When you spin a magnet you create an electric field.  The electric field across a newly formed neutron star is enormous.  That field accelerates vast numbers of  charged particles to stream outwards from the magnetic poles.  However, the powerful magnetic field lines force those particles to move in a spirals as they stream outwards.  When charged particles move in spirals they induce electromagnetic waves -- light.  And those light waves travel in straight beams emitted from the magnetic poles of the neutron star.

Those beams of light carry away some the rotational energy of the Neutron star.  This creates a drag on its rotation.  But given that the star contains a solar mass of neutronium spinning at thousands of RPM, it has plenty of kinetic energy to spare and so the reduction in rotational velocity is very gradual.

If the magnetic poles of the neutron star are not perfectly in line with its spin axis, then those beams of light swing around through space like a lighthouse beacon.  If they happen to be in line with the Earth, we see the object emitting pulses of light as the beams pass by.  We call these pulsating stars Pulsars.