An Offset Smoker has two chambers. The main chamber used for cooking and a separate firebox that is attached to but OFFSET (hence the name) from the cooking chamber.
The fuel, typically charcoal or wood, is placed in the firebox. The temperature is controlled by adjusting the air flow using the damper in the side of the firebox.
The meat is placed in the cooking chamber. Heat and smoke flow from the firebox beneath and above the meat and out the exhaust.