When a VERY massive red giant explodes (as a Type II supernova), its collapsing core MAY either become a neutron star OR a black hole. Whether it ends up as a neutron star or black hole depends on its mass. If its mass is less than about 3 solar masses, gravitational contraction will stop when it's basically a dense sphere of packed neutrons--i.e. a neutron star. If its mass is greater than about 3 solar masses, gravitational contraction will continue until its volume decreases to zero--i.e. a singularity. This is a black hole.
A black hole does not give off light because inside a certain radius, called the Schwartzchild radius, nothing--even light--can escape the black hole.