White pepper, like black pepper, is made from the berries of the pepper plant, also known as the Piper nigrum. Unlike black pepper, however, white pepper comes from berries that are picked at full ripeness. These berries are then soaked in water to ferment. Finally, the outer layer is removed leaving only the inner seed.
Because the skin is removed, some of the flavor is taken, including the piperine. As a result, white pepper tends to be more mild than black pepper.
There are a number of reasons you might choose to use white pepper over black pepper. If you want to get the flavor without the heat or color of black pepper, you'll want to use white pepper.