Antibiotic resisting bacteria are scary indeed. They arise through the evolutionary pressure we put on them with treatments that seek to destroy them. With each reproduction, a bacterial population may gain beneficial mutations that allow the population to survive, pass on those resistant genes, and become resistant.
Bacteria are so good at this for two reasons. First, bacteria can share sections of their DNA between species, making the transfer of resistant genes much easier and faster. Second bacteria evolve very quickly. If you put a single bacterium in an optimal growing environment, within 12 hours you could have as many as 68,719,476,736 copies of that original cell with approximately 1 mutation per million copies. That creates the likelihood of tens of thousands of mutations, each of which might produce a resistance trait to fight off an antibiotic.
To curb this, you should continue your entire regimen of antibiotics (if you are on them) for the full term, even if you start to feel better. By stopping once you feel OK, you are allowing some of the stronger bacteria that survived the initial bombardment a chance to recover and become resistant. You should also only take antibiotics if you have a bacterial infection. If you have a virus, an antibiotic will not help and will only contribute to resistant mutations.