The theory behind fasting and cleansing is that when you fast or cleanse, you are giving your digestive systems and organs a chance to rest rather than continuously try to keep up with the ongoing process of breaking down everything you eat. During this down time, the body has a chance to repair, detoxify, or rejuvenate itself. In conjunction with fasts and cleanses, there are certain exercises and herbs used to enhance detoxification of the organs.
There are a number of methods for detoxifying, including liquids-only diets; organ-specific cleansing techniques; ingestion of fibrous or purging natural substances to clean out the digestive tract; flushing the digestive tract with water (colon hydrotherapy, colonics, enemas, etc), and exercises that stimulate natural detoxification of the body.