Anaerobic means "without oxygen." An anaerobic exercise is any exercise that requires short bursts of power, such as all-out sprinting or very heavy weight-lifting, which do not require a significant increase in oxygen delivery to the muscle.
The ability to perform this type of work depends instead on energy sources stored in the muscle. Because this energy supply is limited, anaerobic exercise can be sustained for only short periods of time. In reality, most exercise is a combination of aerobic and anaerobic exercise. The amount of each is dependent on how hard and fast the exercise proceeds.
With a primarily anaerobic exercise such as sprinting, after about 90 seconds, you begin gasping for air and feel a burning sensation in your lungs your body is forcing you to stop exercising. During an aerobic workout, the point at which your oxygen supply runs out and you slip into using stored energy is called your anaerobic threshold. If you are out of shape, your body is not very efficient at taking in oxygen, and you hit your anaerobic threshold while exercising at very low levels of intensity. In other words, any mismatch between oxygen demands and your ability to supply oxygen is met by anaerobic sources until they run out. As you become more physically fit, you are able to go farther faster and yet still supply oxygen to your muscles, with less need to use limited amounts of stored energy.
Anaerobic training has always been a part of training for competitive athletes. Recently it has been found to enhance fitness for people just looking to get into better shape. The term used most often is interval training -- bursts of very high intensity exercise combined with aerobic recovery. Probably best to do interval training no more than 3 times per week. The short bursts can put a lot of stress on muscles. Similar to resistance training, waiting 48 hours between sessions is best. You can do aerobic exercise every day.