Antibiotics function in a wide variety of mechanisms, but most generally slow down reproduction by interfering with some cellular process (e.g., cell wall , or microtubule formation, etc.) -- that means that the bacteria are still growing, just slowly enough that the immune system of the fishes is capable of dealing with the pathogen faster than the pathogen can reproduce. This is the "normal" state of affairs, and when pathogens are in low concentration within the body, the immune system mobilizes to destroy them. If for some reason the pathogen gets a head start, they can reproduce faster than the local immune system can deal with them (an infection). In most cases the immune system can draw on resources from other areas of the body to deal with the infection and it can be stopped, but once the infection gets rolling, most pathogens can reproduce faster than the immune system cells, and they can run rampant in the host. The idea of using antibiotics is to mess with the reproductive cycle of the pathogen enough that the table is turned and the host immune system becomes the more efficient of the two. In general antibiotic doses are calculated such that reproduction is slowed to the point where the pathogen dies before it is able to complete its life cycle and the treatment last long enough that those individuals that manage to survive are eradicated by the host immune system. That's why your doctor (should!) alway give you enough antibiotic to last well into when you're feeling better, and why you should always take your prescription until it's finished rather than quit taking the pills when you feel better.
