The Air Force Cross is the second highest military decoration that can be awarded to a member of the United States Air Force. The Air Force Cross is the Air Force decoration equivalent to the Distinguished Service Cross (Army) and the Navy Cross (Navy and Marine Corps).
The Air Force Cross is awarded for extraordinary heroism not justifying the award of the Medal of Honor. It may be awarded to any person who, while serving in any capacity with the U.S Air Force, distinguishes him or herself by extraordinary heroism involving one of the following actions:

▪ In action against an enemy of the United States
▪ While engaged in military operations involving conflict with an opposing foreign force
▪ While serving with friendly foreign forces engaged in an armed conflict against an opposing armed force in which the United States is not a belligerent party

Originally entitled the "Distinguished Service Cross (Air Force)", the Air Force Cross was first proposed in 1947 after the creation of the United States Air Force as a separate armed service. In July 1960, the name of the decoration was officially changed to the Air Force Cross. The first award of the Air Force Cross was the posthumously made to Major Rudolph Anderson for extraordinary heroism during the Cuban Missile Crisis.
Additional awards of the Air Force Cross are annotated by oak leaf clusters, and the reverse of every Air Force Cross is engraved with the recipient's name.

More links about the Air Force Cross, it's recipients, and the official U. S. Air Force site.