The best I can explain the actual physics would be that some interactions at the impurities cause electrons to form "wires" of superconductivity in one axis across them. This isn't unheard of in existing materials, but the problem is that in those materials they tend to be isolated "wires" and even tiny disturbances throw the whole thing off.
But that in this material, the way these impurities forms creates a mesh of these "wires" where charge/magnetism can jump. Subsequently, it's resistance to disturbances climbs dramatically, as alternative superconductive paths can be taken as any disturbance propogates through a given part of the material.
They now believe we can use this knowledge to intentionally construct even more materials with this behavior.
And because I never stop finding it hilarious... Part of the preparation of the material is repeatedly taking a piece of scotch tape to a thin strip of the graphite, removing the top layer to make it extra thin.
The parts of my comment that are not quotes are just reasons to not immediately dismiss it, like many other "keystone" technology discoveries.