Vermicomposting is the breaking down of organic material through the use of worms, bacteria, and fungi.  In nature, organic matter is decomposed through these organisms.  By managing vermicomposting you are essentially speeding up mother nature's process of breaking down organic matter.  The end product of vermicomposting is a substance called vermicompost or worm castings.  This is a nutrient rich organic substance that can be added to soil to increase it's organic matter content and available nutrients.  A common way to use this process is to build "worm bins"; basically boxes that contain worms.