First Shirt is military slang for the First Sergeant of a unit of the United States Army, Air Force, or Marine Corps. In this context, the title "First Sergeant" refers to the senior non-commissioned officer of the unit, rather than specifically to the rank of First Sergeant. A "First Shirt" may have the rank of First Sergeant, but that is not required.
The First Sergeant is the formal bridge between the unit's enlisted personnel and the commander. As he is on daily speaking terms with the commander, he will have more authority and influence than his nominal rank would give.
The term "First Shirt" is most often associated with the Air Force, but is also used in the Army and Marine Corps, and originated before the Air Force was made a separate service.
One origin is that when the Army's 15th Infantry Regiment was stationed in China, the unit laundry was taken to local cleaners. The soldier with the most stripes on his shirt (the first sergeant, six stripes total) had his uniform cleaned and pressed first, hence the term "first shirt".
Another origin story derives the term from work details. This leader of a work detail would keep his shirt on, while the other member of the detail wore only t-shirts. The leader thus became referred to as "the shirt", as in "go get me the shirt."
The First Shirt, often further shortened to "Shirt," handles many administrative duties and administers corrective actions when necessary. To be told "See the first shirt" generally means one is in trouble.
A very large unit may only be authorized one "First Shirt", but need similar figures in its sub-units. These unofficial "Shirts" are informally called "Under-shirts" or "Tee-shirts."
One duty of a First Shirt is to select and train these "Under-shirts", finding and mentoring those who have the aptitude to serve as future First Shirts.