Definition
The tendency of a spinning mass, such as a propeller, to resist a change in the direction of its axis and, when a force is applied to tilt that axis, to react with a force felt 90 degrees ahead in the direction of rotation. In a propeller-driven aircraft, this means a yawing or pitching input applied to the propeller disc produces a reaction in a different plane than the one in which the force was applied.
Plain English
A spinning propeller behaves like a gyroscope. If you try to tilt it one way, the aircraft reacts as if you had pushed it ninety degrees later in the direction the prop is spinning. So a pitch input can show up as a yaw, and a yaw input can show up as a pitch.
Context Anchor
Seen in discussions of propeller airplane handling, especially takeoff, tailwheel operations, and rapid nose-up or nose-down changes.
Derivation
From the Greek gyros, meaning ring or circle, and skopein, to look at -- the original gyroscope was an instrument for observing rotation. The term carries over to anything spinning fast enough to display the same physical behavior, including a propeller.
Why Pilots Care
It produces unwanted yaw or pitch changes that must be corrected with rudder or elevator, especially during tail raising in tailwheel airplanes.
Analogy
A spinning bicycle wheel is harder to twist than a wheel that is not spinning. If you try to tilt it, it pushes back in a direction that may not feel obvious at first. A spinning propeller does something similar on an airplane.
Intuition Check
Do not confuse gyroscopic action with engine torque. Torque is the twisting reaction from the engine and propeller; gyroscopic action is the turning effect that appears when the spinning propeller is tilted.
Example Sentence 1
As the tail came up on the takeoff roll, gyroscopic action caused the nose to swing left, and the pilot corrected with right rudder.
Example Sentence 2
Pushing the nose over in a dive creates a right yaw tendency that the pilot counters with left rudder.