Plain English Meaning
The line a spinning wheel turns around — like the line through the middle of a spinning top, from top to bottom. In a gyroscope, this line stays pointed in the same direction, and that's what makes the instrument useful.
Full Definition
The imaginary straight line through the center of a spinning gyroscope around which the rotor turns. The spin axis defines the direction the gyroscope is pointing and, due to rigidity in space, tends to stay fixed relative to space unless acted upon by an outside force.
Context Anchor
Seen in discussions of gyroscopic attitude indicators and how they stay oriented while the airplane pitches and banks around them.
Derivation
“Spin” means to turn rapidly. “Axis” comes from an old word meaning an axle or central line of . Together, “spin axis” means the central line around which something is spinning.