Chandrasekhar (or Chandra for short) 's most notable discovery was his finding at the age 19 (when he was going to England from India as student to continue his studies in a college), that if a star mass is big enough (more than ~4 times the mass of the sun), at the end of its life cycle it wil not turn into a White Dwarf. This limit is related to what is known as the Chandra's Limit.
Average size stars such as our sun at the end of their lives after shedding some mass will simply collaps and become a ball of mostly carbon. They have the size of the earth and are at very high surface temperature of ~30,000 degrees. This is known as a White Dwarf. What holds them against gravitational collaps is the very intersting force of electron degeneracy (which is due to statistics of a class of particles known as Fermions, and is calculable in Quantum Mechanics).
When a star nears its end of life, it sheds some of its mass. After such event it begins to collaps. At this point, Chandra proved, if the remnant mass is 1.4 times the mass of the sun the collaps cannot be stopped by the electron degeneracy force. It will continue to collaps. This collaps leads to formation of either a Neutron star or a Black Hole.
Neutron stars have a size of ~10 kilometer or so but a mass of upto several times the mass of the sun. So each tea-spoonful of them can weigh millions of tons.
Black holes have no size. So in a way they leave this universe and what is left from them is their intensive gravitational force. They cannot be seen because light cannot escape from them.
The formation of a Neutron star or a balck hole is normally preceded by a gigantic explosion known as Supernova. Such events are so powerful that for few seconds the star becomes brighter that the whole galaxy in which they reside. It can destroy all signs of life within a radius of ~50 light years. Let's pray nothing like that will happen in our cosmic neigborhood!!!
The closest star to us is about 4 light years away.