The exact definition of hypergiant stars is somewhat nebulous. They were first identified separately from other supergiant stars because of their significantly large luminosity and mass as compared to similar stars.
Creation of Hypergiant Stars
All stars spend the majority of their lives on the main sequence. However, once the hydrogen fuel in their cores are depleted they will leave the main sequence and evolve into different types of stars all together. However, the process that ensues, is completely dependent on their mass.
Once high mass stars have exhausted the hydrogen fuel in their cores they expand into much larger supergiant stars and begin fusing helium into carbon and oxygen in order to avoid gravitational collapse.
At this stage they will oscillate between the red supergiant and blue supergiant phases as the fusion rates in their cores vary for various reasons. (They will also appear as yellow supergiants as they transition between the two.) The different colors are due to the fact that the star is swelling in size to hundreds of times the radius of our Sun in the red supergiant phase, to less than 25 solar radii in the blue supergiant phase.
In these supergiant phases the stars are losing mass quite rapidly, and therefore are quite bright. It was noticed though, that some of the supergiants were brighter than expected, and follow up observations revealed that they were also some of the most massive stars ever measured.
With some of these stars exceeding 100 times the mass of our Sun - with the largest some 265 times its mass - they were incredibly bright.
It was these characteristics that gave rise to a new classification of star - hypergiants. These stars are essentially supergiants (either red, yellow or blue) that have very high mass and high mass-loss rates (effectively making them very luminous).
Death of Hypergiants
Because of their high mass and luminosity, hypergiants only live a few million years; quite short compared to the billions of years that stars like our Sun will exist.
Eventually the core will fuse heavier and heavier elements until a predominantly iron core is reached. At this point, the endothermic nature of the iron fusion reaction means that fusion can no longer sustain the hydrostatic equilibrium that prevents the star from collapsing upon itself.
The resulting core collapse causes a supernova explosion of incredible magnitude. In fact, some theorize that instead of a typical type II supernova either a Gamma-ray Burst (GRB), sometimes called a hypernova, occurs.