Antibiotic super-bugs are bacteria that have evolved a resistance to antibiotics. They're dangerous because if you get infected by them they will be immune to the medicine the doctor gives you.  

Bacteria evolve very quickly, which is why these bugs appear.  You can reduce the level of antibiotic superbugs by only taking antibiotics when absolutely necessary (when a doctor tells you), and NEVER taking more than the doctor prescribes. The more antibiotics these bacteria are exposed to, the faster they'll evolve. 

Basically, when a person gets sick from anti-biotic resistant bacteria, there is no medicine strong enough anymore to kill the bacteria. The person will get much sicker, and perhaps die.

So, as said above, we need to prevent the creation of these superbugs, or we won't have any way to make these sick people better.

As sarahtonin said above, one of the problems is the over use of antibiotics, but it isn't just from perscriptions or human use.  Another source that's a problem is in the over use of antibiotics in farm animals (cattle, pigs and poultry).  With increased exposure bacteria are able to evolve more quickly than we can develop new medicaitons.  It has only been in the last century that we were able to use antibiotics to treat many who would otherwise have died, but if we continue to abuse them, we will have the same issues even with antibiotic treatments.