Supernovae are the most dynamic and energetic events in our Universe. During a supernova event, enough light is released is outshine an entire galaxy of billions of stars. As these events have been studied, it has been determined that there exist two different types of supernovae, each with their own particular characteristics and dynamics.
Type I Supernovae
Stars, like our Sun, spend most of their lives on what is known as the main sequence. The main sequence begins when the star initially forms -- igniting nuclear fusion in its core -- and ends once the star has exhausted the hydrogen needed to sustain fusion and begins fusing heavier elements.
Once a star leaves the main sequence it will follow a particular path that depends on its mass. For type I supernovae, we are concerned with stars that are no more than about 1.4 times the mass of our Sun. These stars, like our Sun, will leave the main sequence and go through several phases as it fuses elements up to Carbon.
At this point the core of the star is not at a high enough temperature to fuse carbon, and enters a super red-giant phase and the outer envelope of the star slowly dissipates into the surrounding medium and leaves a white dwarf (the remnant carbon/oxygen core of the original star) at the center of a planetary nebula.
If the remaining white dwarf is in a binary system -- that is, if it orbits another nearby star -- the white dwarf can accrete material from its companion. Basically, the white dwarf pulls material off of the other star because of the white dwarf's intense gravity.
The material is pulled into a disk around the white dwarf (known as an accretion disk) and as the material builds up it falls on to the star. Eventually, as the mass of the white dwarf increases to the Chandrasekhar limit (1.38 times the mass of our Sun), it will erupt in a violent explosion known as a type I supernova.
There are some variations of this type of supernova, such as the merger of two white dwarfs (instead of the accretion of material from a main sequence star). It is also thought that type I supernovae encapsulate the infamous gamma-ray bursts (GRBs). These events are the most powerful events in the Universe, outshining the entire Universe in a single second. However, GRBs are likely the merger of two neutron stars (more on those below) instead of two white dwarfs.
Type II Supernovae
Unlike type I supernovae, type II supernovae are the result of an isolated star reaching the end of its life. Whereas stars like our Sun will eventually lack enough energy in their cores to sustain fusion past carbon, larger stars -- more than 8 times the mass of our Sun -- will eventually fuse elements all the way up to iron in the core.
Once the fusion ceases in the core, the core will contract due to the immense gravity and the outer part of the star "falls" onto the core and rebounds to create a massive explosion. Depending on the mass of the core, it will either become a neutron star or black hole.
If the mass of the core is between 1.4 and 3.0 times the mass of the Sun the core will become a neutron star. The iron core contracts and undergoes a process known as neutronization, where the protons in the core collide with very high energy electrons and create neutrons. As this happens the core stiffens and sends shock waves through the material that is falling onto the core. The outer material of the star is then driven out into the surrounding medium creating the supernova.
Should the mass of the core exceed 3.0 times the mass of the Sun, then the core will not be able to support its own immense gravity and will collapse into a black hole. This process will also create shock waves that will drive material into the surrounding medium, creating the same kind of supernova as the neutron star core.
In either case -- whether a neutron star or black hold is created -- the core is left behind as a remnant of the explosion and the rest of the star is blown into the interstellar material, creating the brilliant images that we see.