Methicillin-resistant Staphylococcus aureus (MRSA) simply refers to the development of antibiotic resistance by a common skin bacteria over the last several decades.
"If it bleeds, it leads" news coverage to the contrary, MRSA is not new, not invariably fatal and not incurable or untreatable.
Staph (as Staphylococcus aureus) is commonly known, is one of the common bacteria found in the environment and on any normal, healthy person's skin. Because it is always on your skin, it is one of the most common bacteria to cause skin infection when you get a scrape, cut or some other break in the skin's surface.
Antibiotics used to treat skin infections can lead to the development of antibiotic resistance in surviving strains Staph. Slowly and steadily over the past few decades, strains that resist common antibiotics have become more and more common. This is an expected evolutionary result of antibiotic use.
At this point, MRSA has become a common cause of skin infections. Fortunately, many antibiotics that are inexpensive, safe and generically available work against MRSA (such as Bactrim and Cleocin). This does mean that if doctors suspect MRSA, they may want to use these instead of the usual ones like Keflex or Amoxicillin.
Otherwise, it is not unusual for normal healthy people to spontaneously carry MRSA, and to also spontaneously stop carrying it. Eradication of MRSA from your home and body is technically possible, but really not practical (industrial-strength showers three times a day for a month, anyone?).