Supernovae are the explosions that happen when really big stars burn through all their usual fuel -- hydrogen -- and are forced to try to consume other elements that don't burn as well or for as long as hydrogen does. The resulting flameout creates a massive explosion instead of the burnout that happens in smaller stars like our sun. When our sun runs out of fuel, it will expand and then burn down to a cinder.
As the story notes, these new supernovae interest astronomers even more that the regular, garden-variety supernova does. When astronomers measure the spectrum of the light produced by an object like a star, the readings will tell them what elements make up whatever it is they are looking at -- different elements absorb different wavelengths of light. The new group has very different spectra than other supernovae, and so far astronomers don't know why, or exactly what to call this kind of supernova.
"Big Frickin' Exploding Star" would be my suggestion, but scientists generally like to use more syllables.