Plain English Meaning
A fast-spinning wheel resists being tipped or turned. Once it is spinning, its axis stays pointed where it was first pointed, even if the thing holding it rolls, pitches, or yaws around it.
Full Definition
The property of a spinning gyroscope that causes it to maintain the orientation of its spin axis in space, regardless of how the supporting structure around it moves. As long as the gyro is spinning, its axis continues to point in the same fixed direction relative to space, not relative to the aircraft.
Context Anchor
Seen in discussions of gyroscopic flight instruments, especially instruments that use a spinning gyro to help show aircraft attitude or direction.
Derivation
Rigid comes from the Latin rigidus, meaning stiff or unyielding. The gyro is not physically stiff in the usual sense; it behaves as if it were rigidly fixed in space because its spinning mass resists any change to the direction of its axis.