An event that occurs late in the lifetime of most stars.
Most of a normal star's lifetime is spent fusing hydrogen into helium in its core. The radiation pressure created from fusion thwarts gravity in the core, keeping it from collapsing past the point early in its life when temperatures and pressures in the core caused fusion to begin.
At some point, however, the star begins to run out of hydrogen in its core. Its outer layers diffuse outward, swelling the star into a red giant. The star's position on the Hertzsprung Russell Diagram migrates away from the main sequence. As the amount of hydrogen dwindles, so does the radiation pressure, and the star's gravity causes the core to resume its inward collapse.
The collapse causes temperatures and pressures in the star's core to increase. Eventually, they reach the point where the fusion of helium to carbon and oxygen can take place. The process of fusing helium happens much faster than the process of fusing hydrogen. In a star whose mass is below 1.44 solar masses1, it essentially happens all at once. An immense burst of radiation blows the outer layers of the star off, turning the system into a planetary nebula with a white dwarf at the center. Any life that survived the red giant stage in the system would be obliterated by this burst, or "carbon flash".
A carbon flash can also occur repeatedly if a white dwarf has a main-sequence star as a companion. The dwarf's gravity strips material away from the companion; eventually it's enough to start fusion back up, and eventually the carbon flash stage is reached, creating a Type Ia supernova event.
1On a bigger star, the cycle continues, fusing heavier elements into still heavier elements until the star explodes as a Type II supernova.