It's simple really. When people are ill in hospital they are often weak and their immune system is struggling to cope with wounds and operations.
Think of the immune system as a defending army. When the body suffers major trauma such as an operation, the army masses at the site of the breach. Sometimes that army is stretched too far and the invading army get the upper hand. In previous days the doctors would come along and help with antibiotics (tanks on the battle field) so that the defending army regained the upper hand. However, this army has stolen the tanks ammunition so they are no longer able to fight in the battle. That's about it really. It's an invading army that comes out to play when the cat's away. MRSA is harmless to healthy people, which is why you get more problems in a place of unhealthy people such as a hospital. You can't defeat it without new antibiotics, and there are none on the horizon.
Even if there were, it would only be a matter of time before natural selection (Darwinian theory)rendered them obsolete.