MRSA refers to a particular strain of staph that has become resistant to some or most antibiotics. From the CDC's website:

Staphylococcus aureus, often referred to simply as "staph," are bacteria commonly carried on the skin or in the nose of healthy people.
Occasionally, staph can cause an infection; staph bacteria are one of the most common causes of skin infections in the United States. Most of these
infections are minor (such as pimples and boils) and most can be treated without antibiotics (also known as antimicrobials or antibacterials).
However, staph bacteria can also cause serious infections (such as surgical wound infections and pneumonia). In the past, most serious staph bacteria
infections were treated with a certain type of antibiotic related to penicillin. Over the past 50 years, treatment of these infections has become more
difficult because staph bacteria have become resistant to various antibiotics, including the commonly used penicillin-related antibiotics (1). These
resistant bacteria are called methicillin-resistant Staphylococcus aureus, or MRSA.

Full article can be found at
CDC: MRSA fact sheet
Nasty stuff and getting a little worse each year. Happy reading.
B.