Copa's got it right on. To expand a bit:
All came about from the "composite wing" concept. General fighting unit is a Wing. Wing comprises of one or more Groups. Wing's found at bases with usually one to a base, running that base. The one Wing usually has 2-3 Groups comprising different duties, such as Operations Group, Logistics Group, Medical Group, etc. Within these groups, there's squadrons. Looking at an Operations Group, you'd have two or more fighter/transport/bomber squadrons. A Wing with all fighter units is called a Fighter Wing. A Wing with different types of aircraft under it's charge is called a Wing. At bases with no aircraft assigned, the Wing running the base is known as an Air Base Wing. Squadrons further break down into Flights, for easier management of personnel and equipement.
Above Wing level, there comes Numbered Air Forces. NAFs are the HQ above Wing level. In the CONUS, in ACC, the 12th AF is the HQ for all west coast/half fighter wings, and the 9th AF is the HQ for the east coast/half fighter wings. Above the NAFs are the MAJCOMS, or Major Commands. Both the 9th and the 12th AF report to Air Combat Command.
So in my unit, going from lowest up the chain of command, I'm in D-Flight of the 354th Fighter Squadron, of the 355th Operations Group, of the 355th Fighter Wing, of the 12th Air Force, of the Air Combat Command, of the USAF.
Clear as mud?