The adjective carotid relates to the two major arteries that send blood to your head and neck. The carotid arteries are very important to staying conscious and alive. Take care of your carotid arteries!
This word is used almost exclusively for the carotid arteries. Those large arteries are vitally important, because they supply blood to your head and neck areas. If the carotid arteries are blocked, you will lose consciousness. If the carotid arteries are severed, you could bleed to death quickly. The root is from a Greek verb meaning stupefy, which makes sense given the stupefying feeling you will get if there's a problem with one of your carotid arteries.