White pepper is the fully ripened peppercorn berry, which is then stripped of it's hull before drying. Black pepper is from the same peppercorn, less ripened before harvesting, and when dried it causes the skin of the berry to blacken. Black peppercorns are left with the skin of the berry intact, while white pepper has no skin after it is ready for use.
White pepper has a milder and smoother flavor than black, as the boldness and sharp bite in the black peppercorn's flavor comes from the hull/skin of the berry itself. White pepper does not have the skin of the berry, so lacks the flavor of the skin. White pepper is most commonly used for chowders and soups, and white sauces, as it does not have as harsh of a flavor, and more specifically, it lacks the hit to the throat that is common with black pepper. It also gives a better presentation in soups and white sauces, not yielding the obvious black speckles when black pepper is used.
Eric