Methicillin-resistant Staphylococcus aureus (MRSA) is the first generation "superbug" that evolutionary biologists are always harping about. We're pretty sure that it first developed its resistance in hospitals, where patients are continually bombarded by antibiotics, the most common class of antibiotics being penicillins (including methicillin). Following the rules of natural selection, most of the staph in patients got killed off, except for a few bugs that could survive the methicillin. This property is called "resistance," and the bugs then procreated and propagated - hospitals are full of MRSA.
Staph, of any form, isn't all that dangerous for the average person. It tends to crawl around on our skin all the time - you've got it, believe me. It only gets into your body when you get a cut or other skin injury, and even then, you can fight it off most of the time. Even if it's MRSA, you can usually fight it off - MRSA isn't stronger in any way but against antibiotics. Which is where the problem comes in. If you can't fight it off for some reason, like you've been having a lot of stress lately, or you have AIDS, or you're elderly, or there's some other reason you have a compromised immune system, then doctors turn to antibiotics. These take out normal staph for the most part (though if you overuse antibiotics you will create MRSA within yourself), but MRSA can't be killed by simple antibiotics, and doctors have to turn to more expensive drugs, that have more side effects. Of course, unless you have a history, doctors won't think of MRSA first, so if you are immunocompromised, MRSA is quite dangerous to your health.
Now-a-days, they've started fighting MRSA with vancomycin - penicillins (including methicillin and amoxicillin) and vancomycin all act to weaken the cell walls - but apparently some VRSA strains have started appearing. In addition, MRSA was at first constrained to hospitals, but has started appearing in the "wild" - in people not in hospitals. Today the CDC issued an alert that a string of cases have been found connected with illegal tatoo parlors - I'm guessing their needles became infected from someone who already had MRSA, and then they reused the needles without proper disinfection. This is yet another reason why tatoo regulation is important, and why you should go to a reputable tat artist (AIDS being the primary reason)!
On a personal note, I actually have some form of resistant bacteria myself. I have a skin condition called hidradentis suppurativa (HS) which affects my apocrine sweat glands. What happens is my body's immune system overreacts to the bacteria normally present there (in my case, a resistant strain of bacteria) and becomes significantly inflamed. I've been taking antibiotics periodically since it first developed around age 13 - so I've been on antibiotics between 2 and 8 weeks out of each year for the majority of my life. Is it any wonder that with this continual dosing of antibiotics that I've developed resistant bacteria in my own body? While I don't have the details of what specifically the strain is, I really expect that it evolved within me, rather than being something I contracted from outside. This is part of why I'm such an advocator for evolution education - it's happening inside me, to my own detriment. Basically none of the traditional antibiotics work for the bacteria in my armpit skin anymore (not amoxicillin, which is part of penicillins, which is part of the class of beta-lactam antibiotics; not cephalexin which is another β-lactam), so we use levoquin, which is in the class known as quinolones - these act by preventing bacterial DNA replication (and hopefully don't stop my own DNA replication). Interestingly, apparently there are a few quinolone-resistant staph strains as well, but thankfully I do not appear to have those in me, though chances are I'll create them eventually. Whee.