This diagram shows the path the intubation tube takes. It passes up and over the epiglottis, down into the glottis, and down into the trachea. This picture even shows how far down the inflated cuff should be in the trachea.
Check out this Cartoon on how your thyroid works. Thyroid issues can get complicated, so this might help explain a little bit better what dotors do not explain to their patients. Check out that T-shirt here: