On a carrier, the Naval Aviator looks over at the Catapult Officer ("Shooter") who gives the run up engines signal by rotating his finger above his head. The pilot pushes the throttle forward, verifies all flight controls are operational, checks all gauges, and gives the Cat officer a brisk salute, continuing the Navy and Marine tradition of asking permission to leave the ship. The Cat officer drops to one knee while swooping his arm forward and pointing down deck, granting that permission. The pilot is immediately catapulted and becomes airborne.
Air Force Pilot:
We've all seen Air Force pilots at the air force base look up just before taxiing for takeoff and the ground crew waits until the pilot's thumb is sticking straight up. The crew chief then confirms that he sees the thumb, salutes, and the Air Force pilot then takes off. This time-tested tradition is the last link in the Air Force safety net to confirm that the pilot does not have his thumb up his ass.
If you've ever seen an Army helicopter pilot preparing for takeoff, you will note that the pilot gives the ground guy a thumbs up before he is given hover and takeoff signals. There are two theories about the origin of this gesture. One is that it is to show that the pilot has identified which of his fingers is the thumb so that he will be able to properly operate his controls. The most compelling theory says that this is to show the ground crewman that the pilot indeed knows which direction is up.
But thanks to all of them.