In order for natural selection to occur, a selection pressure must be present. This selection pressure causes species to die out, and the ones that are able to cope with this pressure have what is called a selective advantage.
In the above mentioned scenario, the selection pressure on bacteria are the antibiotics that kill them. This occurs until some bacteria are born with a genetic mutation that allows them to survive the effect of an antibiotic.
Once this occurs, the bacterium is able to survive while the rest of the bacteria are wiped out by the antibiotic. This bacterium then has all of the present resources available to itself, which means that it can divide indefinitely until resources run out. It passes this antibiotic resistance to its offspring, and a strain of bacterium is formed which is resistant to antibiotics.
