Anaerobic pertains to organisms, such as bacteria, that can live in the absence of atmospheric oxygen. "Anaerobic" is often used to refer to such organisms living in a compost bin and influencing the quality of its decomposition; it also refers to the conditions under which such organisms thrive.
Aerobic compost piles are turned frequently, to avoid compaction and keep oxygen flowering freely through the pile. At the peak of the decomposition process, they become quite hot. By contrast, under anaerobic conditions, fermentation will take place.
While there is a method of composting known as "anaerobic composting," most people who maintain compost bins try to discourage the presence of anaerobic organisms; i.e., most of us practice aerobic composting. Anaerobic composting is less labor intensive (because there's no turning of the pile), but produces an offensive smell. By contrast, properly maintained aerobic compost bins do not produce offensive odors.
