Genetic mutations randomly occur in the population of cells. If, by chance, there is a mutation that gives the bacterial cell resistance to an antibiotic, then that mutation will remain in the population.
This is because it gives the cell a competitive advantage (because it is more likely to survive than its non-resistant counterparts). If it survives, it will divide and pass the mutation on to its daughter cells, which will survive. This keeps happening until an entire population will carry the mutation.
