Animals are fed antibiotics at low doses to make them bigger. No one really knows why this causes animals to grow larger, but it does. The animals, which eat antibiotics, develop resistant bacteria in their gut. Animals, which are then fed to humans, have bacteria that can potentially spread to humans.
Animal feces (which can be antibiotic resistant) are used in fertilizer, which is used in the crops to feed both animals and humans. The antibiotic resistant bacteria can survive on crops and can be consumed by humans.