Radical substitution (or abstraction) involves a radical species removing an atom (often H or a halogen) from a nearby molecule. However, the radical abstraction reaction usually produces a new radical centre which is itself able to undergo a radical substitution. Thus, the scene is set for a cyclical sequence of back-to-back radical substitutions which proceed until one or more of the reagents are consumed. Radical substitutions require a catalytic quantity of "initiator" (a substance which easily fragments into radicals, such as dibenzoyl peroxide) plus heat or UV light to get the reaction going. Radical substitutions are slowly terminated as the various radical centres in the reaction mixture couple together.
For more information look in the Chemogenesis
webbook section on radical