A neutron star (NS) is a object basically of neutrons, the result of gravitational collapse of a star after it has used up the energy that created the pressure to resist such collapse. Its mass is large enough that gravity overcomes electron degeneracy and causes such collapse but not so large as to overcome neutron degeneracy pressure, which prevents them collapsing into a black hole Typical neutron star mass is 1.4 to 3.2 solar masses with a radius on the order of 10 km. Stars with lesser mass that don't collapse remain as white dwarves. Think of a neutron star as roughly "squeezing the Sun so its cross section is about the size of New York City's land area, whereas a white dwarf is more like "squeezing the Sun into the size of Earth". Neutron stars' existence was first proposed in 1934 and the first candidates that have panned out were identified in the 1960s.
Rotation of neutron stars and their magnetic field can make them emit directed beams of EMR whose direction rotates, showing to observers as pulses (pulsars). The magnetic field may be strong enough to affect the trajectory of accretion, channeling it to the magnetic poles. The point where the magnetic field is sufficiently strong to overcome the accreting mass's kinetic energy is called the Alfvén radius.
A portion of neutron stars can be described as a "mass of neutrons", and the density is on the same order as the density of an atomic nucleus. However, the pressures at different depths produce different states of matter with different densities, with less exotic states toward the surface, which is thought to include iron. Deeper, the material can have superfluid (no friction) and superconducting fluid (no electrical resistance) characteristics. Some theories suggest the center can be a "mass of quarks" rather than nucleons, and/or a density at the center is much as six times that of an atomic nucleus.
The term proto-neutron star (PNS) refers to a neutron star at the beginning of its life as it goes through some preliminary phases with some slower shrinking, on the order of its first 10 seconds.