A paper appeared on the arxiv recently (published in Advanced Materials) from a group in Leipzig reporting magnetic measurements that the authors argue are suggestive of some kind of room temperature superconductivity in highly oriented pyrolitic graphite (that's enhanced after a particular treatment involving water). Unsurprisingly, this got a bit of attention. So, what is the deal?
Well, it's been known for a long time that clean graphite has a very large diamagnetic response. That means that when a magnetic field is applied to the material from the outside, the field inside the material is less than the external field. This can happen in a couple of ways. In a type-I superconductor, at low applied magnetic fields, persistent "screening" currents are set up that completely cancel the externally applied field. This perfect diamagnetism is called the Meissner effect, and is a signature of superconductivity. (Why this happens is actually a pretty deep question - just accept for now that it does.)
The investigators have spent a long time staring at the magnetization of their graphite as a function of applied magnetic field and temperature, and they argue that what they see could be a signature of some kind of "granular" superconductivity. This means that the bulk of the material is not superconducting. In fact, you can compare the measured diamagnetism with what one would expect for a perfect diamagnet, and if this is superconductivity, only about 0.01% of the sample is superconducting. Still, the systematics that they find are interesting and definitely worth further investigation. It's important to know, though, that there have been similar discussions for over a decade. We're not there yet.