Plain English Meaning
When a gyroscope is spinning fast, its spin axis tries to keep pointing the same way no matter how you move the case around it. That stubbornness to stay pointed in one direction is what's meant by rigidity here.
Full Definition
The property of a spinning gyroscope that causes it to resist changes in the orientation of its spin axis, allowing the axis to remain fixed in space regardless of how the supporting structure moves around it. This property is the basis for gyroscopic instruments such as the attitude indicator, heading indicator, and turn coordinator.
Context Anchor
Seen in instrument flying when learning how a heading indicator works and why its internal gyro can provide a stable heading reference.