An example of antibiotic resistant traits is the amount of pores a bacteria has in it's cell membrane. To kill bacteria, most antibiotics have to get through the cell membrane, or find an opening in the cell membrane. This makes it so that the bacteria with more pore openings have more chances to let bacteria in and kill them, making it so that more pored bacteria will have more chance of dying compared to less pored bacteria.
As the antibiotics are administered to Addie, the antibiotics are able to kill off the bacteria that are not resistant to antibiotics, leaving some leftover unresistant bacteria along with the majority of the beginning resistant bacteria.
After the antibiotics kill off some of the non-resistant bacteria, the bacteria reproduce again, having a higher percentage of resistant bacteria than before, from some of the non-resistant bacteria having been killed. The cycle repeats, the non-resistant bacteria being killed off while the remaining bacteria are left to reproduce and pass on their traits. Since the resistant bacteria are more likely to survive, after a while, the population becomes only resistant bacteria.
Eventually, through natural selection where the bacteria with stronger traits live to pass on their resistance where bacteria with weaker traits aren't able to pass on their traits before they die, the population becomes consisting of all resistant bacteria, and the population of bacteria becomes resistant to that antibiotic.
After multiple antibiotics and cycles of natural selection, the stenotrophomonas bacteria became pan-resistant, resistant to all types of antibiotics. As a last resort, Addie had to get a lung transplant to remove the infected area