Neutron stars form from stars with masses greater than 1.4 solar masses. When a star bigger than 1.4 times the mass of the Sun reaches the end of its life, the gravity it has squashes it so much that protons and electrons are squeezed into neutrons.
Neutron stars have diameters of a few tens of kilometres, depending on their mass.
Most of the interior of the star consists on a neutron gas at such high densities, it is a fluid. Because a neutron star is so dense though it has an enormous surface gravity which means the escape velocity on the surface of such a star can be 0.8 times the speed of light. Neutron stars can therefore emit light, they are not like black holes in that respect. Black holes are formed from bigger stars - 2.5 solar masses or greater. These stars have so much mass that when they die and get squashed the gravity is so great that light cannot escape.