Radical addition involves a radical, Ri, interacting with pi-system to form a sigma bond and a new radical centre. The newly formed radical centre then abstracts an atom X from X-R to give the addition product and another molecule of Ri. Radical additions propagate in this cyclic or "chain" manner until reagents are consumed or the reaction is terminated by radical coupling. Radical additions 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.
For more information look in the Chemogenesis
webbook section on addition