(Asked by Mike Kelly and Ben Foster)
The Stellar Life Cycle
During the lifetime of a normal star, Hydrogen is "burned" into Helium through the processes of nuclear fusion in the core of a star. This is currently the process which is occuring in the core of our sun.
In about 5 billion years however, enough Helium will have accumulated in the core of the star to begin Helium burning. The Helium burning phase begins and the core contracts (partially because Helium is more dense than Hydrogen). As the core contracts it gets much hotter, and this heat escapes into the vast outer layers of Hydrogen surrounding the core. Much like a balloon filling with hot air, these outer layers expand tremendously. The star becomes a red giant. When our sun becomes a red giant in the distant future, its outer layers may expand out past the earth's orbit! Our planet will be vaporized!

After the red giant phase, the Helium burning continues -- creating an accumulation of carbon in the core. Again contraction and release of heat occurs -- this time blowing off the outer layers of the star completely. All that's left is a small glowing hunk of the carbon core. This carbon core is called a white dwarf, and it takes about 15 billion years to cool off. The star is now "dead".
Not all stars end their lives in this fashion. For stars having more than 15 times as much mass as the Sun, death comes quickly -- and violently.
Supernovae
Stars with more mass have a higher pressure and temperature at their cores, and this allows fusion to occur at a faster rate. After a few million years, a star may reach the Helium burning phase. This proceeds as described above, but doesn't stop! Helium burns into Carbon. Carbon burns into Silcon, Oxygen, Magnesium, and other heavier elements. This proceeds on and on until a large amount of Iron accumulates in the core. Iron cannot fuse into any heavier elements, and yet the core must "try" to contract under the vast temperature and pressures of the heavy surrounding elements. What happens next?
The core begins to contract and pulverizes the Iron into nucleons (groups of protons and neutrons). But the nucleons can only be compressed so far; once a certain pressure limit is reached, the contraction of the core "bounces back" and a gigantic shock wave rips the guts of the star apart. This explosion is called a supernova. The shock wave sets off fusion in the outer layers of the star, creating a tremendous burst of light. During this period of time the brightness of the star increases by a factor several billion -- outshining the combined brightness of the entire galaxy!

Ironically, the cataclysmic destruction brought about by supernovae releases gas and dust which will subsequently clump together to form new stars -- and the process may be repeated. In fact, the presence of elements here on Earth which are heavier than Iron (only the supernova shock wave can create enough energy to fuse Iron into heavier elements) strongly suggests that the stuff around us and what we are made of was once at the heart of one of these cosmic explosions.

--D. Gau