Extinction is when a species or other similar group no longer exists — "The dodo bird is extinct. The species died out centuries ago." Or "Humans hunted that species of bird to extinction." I assume you mean "Extermination." Extermination is the active, willful process of completely killing or destroying something. It is often used with pests (exterminators are people who kill bugs or other vermin in your house).

EXTINCTION means no longer in existence. EXTERMATION, I don't this word. Are you sure of its spelling?