Here is a diagram of a fermenter, the key parts are labelled:
The cooling jacket (labelled here as water column) controls the temperature as the cool water conducts heat from within. The temperature and PH both need to be monitored so that they can be kept at the optimum level for the enzymes. If the enzymes are in their optimum conditions then they will react faster.
Inoculum is the starter culture; basically it helps the fermentation start.
The air inlet gets oxygen into the fermenter. Oxygen is needed for the micro-organisms to respire. A sparger/agitator makes the air into very small bubbles; this means they have a larger surface area and can dissolve easily, so there is better access to oxygen for micro-organisms.
Aseptic conditions are needed as if there were other microbes in the fermenter; firstly they would contaminate the product; secondly they would use up nutrients and oxygen.
Nutrients are needed in the fermenter so the micro-organism can grow.