When we say that a food is "fermented", we generally mean that it has been transformed one way or another by microbes--bacteria, yeasts, molds, or some combination. Molds play a role in the creation of some kinds of cheeses and cured meats (dried sausages, for instance), along with soy sauce, among other things. Yeasts are responsible for anything that contains alcohol, either as an end product or in an intermediate stage (vinegar, for instance, and bread). Bacteria are responsible for things that are sour--from vinegar to yogurt to sauerkraut to mustard to chutneys and condiments like ketchup. Nowadays, short-cut versions of some of these foods are manufactured via processes that do not rely directly on fermentation.
The health benefits of fermented foods can be broken down into a number of categories: