Shock that it may be, these young stylish whipper-snappers could probably not be evolutionarily further from us; they are bacteria. Whilst the DNA that makes up our genome has collected a huge amount of material over the years, including retroviruses that have taken up permanent residence and other repetitive elements of DNA previously labelled as junk, the bacterial genome is a much more stripped down affair. Not only this, but bacteria are very small, smaller in fact than even a single human cell. This allows them to reproduce extremely rapidly. Couple this to the massive bacterial populations that inhabit our bodies (there are in fact more bacterial cells in a human body than there are human cells) and there can be real problems associated with treating infections.
Among a massive population of bacteria there will be variation, and if you take antibiotics some bacteria may be more susceptible and others less so. If you then stop taking the drugs before finishing the course the less susceptible bacteria may survive and due to their rapid reproduction could quickly repopulate the available space producing a wholly resistant population. This is human evolution on speed. Think how long it would take the human population to recover if something came into the environment and killed off all but the most hardy 0.1%; it would be measured in centuries not days. In bacteria it takes closer to hours. In this way, advantageous mutations can rapidly appear in a massive majority of bacteria when a strong selective pressure, like an antibiotic is applied.