Circulatory Organ
You already know that 循環 means "circulation," so adding container makes it what holds things that circulate. They're your circulatory organs. They contain all the air moving throughout your body like a container.
じゅんかんき
This is a jukugo word that uses the on'yomi readings of the kanji. You should be able to read this on your own.
当院には、循環器専門医が五人います。
There are five circulatory organ specialists in this hospital.