An aerobic organism (aerobe) is an organism that has an oxygen-based metabolism. Aerobes, in a process know as cellular respiration, use oxygen to oxidize substrates, like sugars and fats, in order to obtain energy. The aerobic micro-organisms use oxygen in the air the same way that humans do. They breathe air and without air they simply die. The products of aerobic degradation are carbon dioxide, water vapor, a lot of heat and compost. Aerobic organisms are usually found in the top soil because that is where the most air is found.
Anaerobic organisms do not require oxygen for the release of energy from food molecules such as glucose. An organism is described as anaerobic if it does not require oxygen in order to survive. Instead, anaerobic organisms use anaerobic respiration to obtain energy from food. Most anaerobic organisms are micro-organisms such as bacteria, yeasts, and internal parasites. These micro-organisms live in places where there is never much oxygen, such as mud at the bottom of the lake or pond, or in the alimentary canal. Anaerobic organisms release much less of the available energy from their food than do aerobic organisms.
If you take a banana peel and place it into a landfill it would undergo decomposition without oxygen (or anaerobic decomposition). This happens because landfills are designed to be extremely compact, and the circulation of oxygen is limited. "Landfill gas" is one of the by products of anaerobic decomposition and is comprised primarily of carbon dioxide and methane. This effect is so extreme that the anaerobic decomposition of organic waste is the number one producer of methane gas in the US. Methane not only smells, but is also the most potent of all the greenhouse gases (it contributes 25 times more to climate change than carbon dioxide). However, if we were to take the same banana peel and place it into a compost pile it would undergo decomposition with oxygen (or aerobic decomposition). In such an aerobic system the decomposition process relies on aerobic bacteria that break down the organic matter into humus, without any harmful gas emissions. The end product, humus or compost, is a fantastic plant growth agent.