When you have high ceilings, you increase the air volume within a room.

This is important for two reasons. First, what the people inside the room exhale is then a smaller percentage of the total air. However, this can be accomplished with the usual eight foot ceiling simply by making the area larger.

Second, with a high ceiling, there is a better gradient, a more pronounced difference between the air near the ceiling and the air near the floor. This helps the room to create its own weather system, if you will, which helps air circulation and mixing of the air within the room. (And, this helps keep the bad stuff from becoming as concentrated near the people).

These were the other reasons that the cathedrals of Europe have those very high ceilings (in addition to the glorification of God)!

These are the same reasons that most of our churches and old public buildings did too.