A black hole is currently "understood" as a place in the universe where our understanding of the laws of physics breaks down and is no longer true, which makes the question of "understanding" them rather difficult. I think it can be somewhat achieved, though, by looking at the stages a star goes through before it reaches the TOV limit (the final mass limit for a cold neutron star) and collapses to form a "black hole".
So, first you have a happy star, chugging away converting hydrogen into massive nuclear explosions to sustain its core (using fusion). This goes on for a couple of billion years before the star runs out of hydrogen to burn - for fuel, it then turns to heaver particles with more energy in the nucleus, like helium etc., slowly moving it's way up the periodic table in weight as it burns up all of the lighter elements. This causes the surface of the star to expand because the heavier, more energetic particles give off more powerful nuclear explosions at the core. This is all fine and dandy until it reaches Fe (Iron) - Iron has too much energy in it's nucleus to be used as a fuel source for nuclear fission, and the explosions quickly become too violent and unstable in the core, causing the star to explode - this is called a supernovae.
For most main sequence stars, it stops here - these aren't the stars you're asking about though. The ones you're asking about are the super-giants, 15 to 30+ solar masses while healthy, and their deaths get very interesting. What happens first is a rather remarkable thing; there is so much matter that is exploding out of the star (30 suns worth to be exact) that the gravity exerted by all of this mass is unfathomably huge - so great, in fact, that it stops the supernovae in its tracks, while it is still expanding, and forces it to begin compressing again. There is one huge, important difference this time however - there are now no explosions at the core of all of this rapidly compressing matter to stop it from shrinking once it reaches it's original size, so it keeps on compressing and getting smaller and smaller.
Now we encounter the final vanguard against black holes - the degeneracy pressures. These are forces that arise as a result of something we call the "Pauli exclusion principle", or the principle that "two fermions with the same half-integer spin cannot occupy the same quantum space at the same time" - this means that you can't have two or more electrons in the same spot at the same time (or 2+ protons in the same spot, or 2+ neutrons in the same spot). The reason that this becomes relevant to us is because the star-matter will continue compressing and smashing together with nothing to stop it until it is just a sea of free-floating electrons and protons - this is called a White Dwarf. The reason that some would-be black holes stop collapsing here is because of the Proton/Electron Degeneracy Pressures, meaning that the protons/electrons couldn't compress any further due to gravity without two being in the same space, violating the Pauli exclusion principle, so there is actually a force (or pressure) that arises to stop this from happening. This "degenerate force" is unimaginably strong and can stop all but the most massive stars from becoming a black hole, however there is one even greater force in the universe that stops an even more massive body from collapsing - namely, Neutron Degeneracy Pressure and Neutron Stars.