Tracheal obstruction by a large piece of food typically involves obstruction of the larynx. The larynx is found superior to the trachea in the respiratory tract. When we swallow, the epiglottis is usually seals the opening. But when we swallow, sometimes the epiglottis fails to do so, especially when we try to breath as we swallow.
This is why we do not recommend talking while your mouth is full. Since we need air as we speak, food can accidentally fall into the larynx.