The magnificant fireball which has been burning for roughly 4.5 billion years, which we call the Sun, is a G2 type star, which means that it is a main sequence yellow star whose surface temperature is around 10,000 degrees F/5700 degrees C.
In about 5 billion years, the Sun will have used up it's hydrogen and begin burning helium, at which point it will fall off the main sequence, swell up to a red giant and start the slow and occasionally violent process of dying. Earth will be obliterated as a result.
In a spectacular supernova event, a binary system of stars (two stars in close proximity with eachother), interact in a manner which is detrimental to the health of one of the stars. The star with the most stellar mass, and thefore gravitational pull, pulls off the material from it's neighboring star. The hydrogen in the dominant star reaches critical mass and explodes, obliterating the star in the process and releasing an utterly astounding amount of energy. The formation of the infamous Crab Nebula is a result of a supernova event.
Because low-mass stars have insufficient mass to turn carbon into nuclear fuel, the remaining cinder (that used to be in the star's core) simply cools down, slowly, for the rest of eternity. These stellar corposes are called white dwarfs.
When a star's core implodes, and it less than the mass of three solar masses (three times as massive as our Sun), the core stops collapsing once the neutrinos formed in the implosion can no longer be squeezed together tightly by gravity. What then remains is a neutron star. A tiny object - just a few miles in diameter - that is a million times denser than a white dwarf (which is incredibly dense). If you tried to extract a tablespoon of neutron star, you'd need some heavy lifting equipment, because that tablepsoon would have about a billion tons of densely packed neutrons on it.
Neutron stars spin incredibly fast and have immense magnetic fields. From whch energy escapes at the magnetic poles. As the neutron star's rotation whips it around (up to a hundred times per second), we are able to pick up the energy here on Earth as pulses - which is why these stars are also called pulsars. These energy pulses are often radio, gamma, or X-ray waves, but a few of them pulse visibly.
What if the core of a star is greater than three solar masses during a critical mass implosion? Well, gravitational forces compress the core into an infinitely dense, dimensionless point with such crushingly high gravity that not even light can escape it's clutches. We commonly refer to this pehonomenon as a black hole singularity.