Black holes are probably the most interesting entities in the universe. But exactly what is a black hole?
In our massive universe, there are many stars like our sun, which provide warmth and light to the rest of the nearly empty universe. Some stars, however, can be smaller, bigger, or much bigger than our sun. This video uploaded by patdesignnet shows this well. 
The key to the formation of a black hole lies in how big the star is when it dies and how massive the core is left behind.
Our sun, and similar stars, will leave behind a small core after its death that can eventually become a white dwarf. Bigger stars (10 times or more the size of our sun) will leave cores that form neutron stars. Stars much more massive are the ones that win the lottery: those stars, due to massive gravitational pressure, will form a black hole.
A picture showing what happens after a star dies. Picture from MSN.com
The physics behind this progression is actually determined by an intimate relationship between quantum mechanics and gravity.
In order to become a black hole, matter has to bypass two barriers: electron degeneracy pressure and neutron degeneracy pressure.
Depending on the size of the star, the forces that hold the entity stable is shown here. One solar mass is equal to the mass of our sun. Image from Dr. David P. Bennett, from the University of Notre Dame.
White dwarves are held stable against gravity due to electron degeneracy pressure. The gravity of the white dwarf forces matter to compress smaller and denser, and consequently the electrons within the atoms will move around faster because there is less room to move around; therefore, the electrons will exert a force outward to counter gravity.
When a larger star dies (10 times our sun), the electrons have no more space to move and therefore collapse into the nucleus to fuse with the protons to form neutrons. This is when a neutron star can form. A neutron star is literally a mass of neutrons; there are no protons or electrons present because gravity has forced them to merge together to form neutrons. However, gravity cannot proceed further because of neutron degeneracy pressure, which is similar to electron degeneracy pressure.
When an even larger star dies (100 times our sun), the neutrons also are forced by gravity to merge together. However, they do not merge to form new particles; instead, all the matter of the star is condensed into a single point called a singularity. This is gravity’s ultimate victory.
Here is a video describing the formation of black holes by Discovery TV. 
Physicists, since the time of Einstein, have long sought to combine the forces of the very small and the very large into the elusive Theory of Everything, which is practically the only aspect of Physics we do not understand.
The importance of studying black holes is to gain insight and understand what and how the law governing the very small and the very large are unified.
Hopefully, by using black holes, we can complete the picture of Physics as we know it.
– Tony Hui
Acknowledgements:
I would like to thank Dr. Ludovic Van Waerbeke for teaching me about the fascinating story of black holes in Astronomy 102. All the information found here is based on from Dr. Waerbeke’s lecture slides and from his lectures.
