Fermentation is controlled microbial activity. Bacteria or yeasts convert sugars into acids, alcohol or gas, and those products both change the flavour of the food and make it inhospitable to the organisms that would spoil it. Sauerkraut, yoghurt, cheese, soy sauce, beer and bread all belong to this family.
Lactic acid fermentation
The one most vegetable recipes mean. Lactic acid bacteria already present on the vegetable convert its sugars into lactic acid, dropping the pH until competing organisms cannot grow. Salt and the exclusion of air steer the process: the salt slows most spoilage organisms while the lactic acid bacteria tolerate it, and submersion keeps the surface anaerobic.
Fermentation is not pickling
Pickling means preserving in acid. A fermented pickle makes its own acid; a vinegar pickle has acid added to it. The two produce different flavours and are stored differently, which is why a recipe for one is not a recipe for the other.
Safety is a measurement, not a feeling
Fermentation guides give brine percentages and target pH values because those are the things that determine whether a ferment is safe, and neither can be judged by eye. This is the point where a book earns its place over a recalled instruction.