Most commonly, brightening is used to mean lightening, fading, or, at its most extreme cases, bleaching. Brightening is also used to describe products that may block the production of pigment and/or lift pigment out of the skin (think dark spots from the sun or acne scars).
A chemical peel is a technique used to improve the appearance of the skin on the face, neck or hands. A chemical solution is applied to the skin that causes it to exfoliate and eventually peel off. The new, regenerated skin is usually smoother and less wrinkled than the old skin.