There are several types of supernovae. The Type 1a variety doesn't form as the result of the explosion of a massive star. Instead, it develops via the destruction of a white dwarf orbiting a younger binary partner, or two white dwarfs slamming into one another.
In the former case, material is stripped from the binary partner until the material reaches "critical mass" around the white dwarf. At that point, the supernova ignites, burning brightly for a short period until all that's left is remnants, known as nebulae.
That much physicists understand, but the underlying physical mechanism is complex, and remains mysterious. A better understanding of the processes that give rise to Type 1a supernovae would enable us to make more precise distance measurements in space, since these objects are used as standard candles.
Of particular interest is a phenomenon known as deflagration to detonation transition (DDT). Deflagration is essentially a slow burn, or "subsonic combustion," in which a burning substance heats the next layer of cold material until it ignites. That's the process behind internal combustion engines, for example, or the pyrotechnics of fireworks.