White dwarf stars are usually what's left over after middle-sized stars burn out. Our sun is likely destined for white dwarf status several billion years from now.
Stars burn through nuclear fusion and although they are massive, after a long enough time they run out of the elements they fuse for fuel. Big stars blow up in a nova or supernova. Medium-sized stars flare up into a planetary nebula as they expel their outer layers (for the curious, this event is what will probably destroy the Earth or at least render it unlivable). The leftover interior core is made up of much heavier elements than the hydrogen and helium the star has been burning, and those elements are now affected by gravity since there's no longer any expansion pressure from fusion energy. They collapse, squeezing the mass of half the sun into a sphere the size of the earth. Most of the time, their remaining cores are made up of the elements oxygen, neon and magnesium. The little hydrogen or helium that's left forms a thin atmosphere.
Except for a white dwarf known as SDSS J124043.01+671034.68. About 1200 light-years from Earth, its atmosphere is almost entirely oxygen. Normally, the heavier oxygen atoms are compressed by the white dwarf's gravity so that they are trapped in the core, but not for this particular white dwarf, and astronomers don't know how it happened. Carbon fusion could produce an oxygen atmosphere -- the star could have burnt carbon in its last days before collapsing, in other words. But white dwarfs of SDSS J124043.01+671034.68's size don't undergo carbon fusion as it's currently understood. In fact, white dwarfs that size usually don't have oxygen at all.
It's all very head-scratchy for astronomers and physicists, and the ones quoted in the story sound like they're having all kinds of fun trying to figure out just exactly how SDSS J124043.01+671034.68 is going to mess up the way we have understood some things about fusion and star structures. But then, nothing makes a scientist giggle like discovering something that kicks over a bunch of theoretical applecarts.
Even though it's got an oxygen atmosphere, you should put aside ideas about vacationing on this particular spot. Since the surface gravity on a white dwarf is about 100,000 times that of Earth, you wouldn't even have the strength to inflate your lungs to inhale in the milliseconds you'd have before your body compressed like one of those vacuum storage bags you see on TV. Plus, the temperature may be less than a regular star, but it's still around 180,000 degrees Fahrenheit. So any attempt to visit SDSS J124043.01+671034.68 would indeed leave you a hot mess.