MRSA (a lot of people just say "mersa") is a form of staph bacteria that have become resistant to almost all of the antibiotics that we use in medicine every day. It's been doing that over about 60 years, largely without our really noticing or understanding how big a threat it has become. It's a threat to people who are in hospitals, but in recent years it's also become a threat to people out in the everyday world. It kind of takes people by surprise. It often affects, for instance, people in gyms or kids who play sports.
The macro-answer is that MRSA is the leading edge of a really international epidemic of drug-resistant organisms that are getting worse and worse, both because they're getting more resistant and also because we've, for the most part, stopped making antibiotics. So as as the bugs get more resistant, were running out of ways to treat them, because there's no new drug coming along. And as if that weren't all bad enough, it takes in not just human medicine and how we use drugs there, but also increasingly how we use and misuse drugs in farming around the world.
A few recent preoccupations basically account for MRSA’s potency: for one, hospitals’ inability to keep its patients from being infected. (For more, recall this Washington Monthly article about hospital-borne infections, particularly from MRSA.) The worst aspect of MRSA—as opposed to other inefficiencies in the system—is that these antibiotic-resistant bacteria become all the more resistant the longer hospitals allow them to hang around. Scanning someone unnecessarily and exposing the patient to more cancer risk is one thing that affects only that patient alone; getting someone infected with MRSA increases the risk that someone down the line will get a nastier version of the thing. (Scientific American has a similar report—sadly only in preview version—about a bug called Klebsiella pneumoniae.)
The other recent preoccupation that accounts for its potency is the apparent lack of progress on antiobiotics, which I suppose has stagnated like the rest of the drug industry’s advances. There’s a Great Stagnation angle there, of course. Are antibiotics like some other drugs—not profitable enough to develop? Or has the drug industry just reached a frontier of knowledge beyond which they’ve had trouble trailblazing? You don’t hear a lot of media coverage about the latest antibiotic drug trial, as you do for cancer, diabetes and other media-friendly diseases; but is that because there is none or because the media just isn’t paying attention? This editorial in a Connecticut outlet suggests the problem is insufficient profits (because you only take an antibiotic for a few days) and thorny regulatory barriers, which in turn suggests, perhaps, a prize incentive rather than a patent incentive?