In this sense, "air" refers to a simple, often lyrical, melody or song. It's typically a memorable and harmonious composition.
Here are a few sentences demonstrating this usage:
The musician composed a beautiful air that brought tears to the eyes of the audience.
She hummed a lively air as she went about her morning routine.
The folk singer performed a haunting traditional air about lost love.
After one inserts their pinkie finger into the rectum of their sexual partner and has to hold their pinkie out to avoid getting fecal matter on their other digits or themselves while finishing sexual intercourse.
Frank gave Cindy the old two in the pink one in the sink and had to air pinkie it while they finished having sex. He then scrubbed his finger with bleach.