Plain English Meaning
The gyro is held in just one swiveling frame, so it can lean in only one direction. That one direction of freedom is what lets the instrument measure turning.
Full Definition
A mounting arrangement in which a spinning gyro is supported in only one pivoted ring, allowing the gyro to tilt about a single axis. This restricted freedom limits the gyro to sensing motion about that one axis, which is why turn-and-slip indicators use a single-gimbal gyro to detect yaw (turn) only.
Context Anchor
Seen in descriptions of how the turn-and-slip indicator works inside the instrument panel.
Derivation
Gimbal comes from an old French word for a jointed link or pivoted ring. 'Single' simply means one such ring is used, rather than the two used in attitude and heading .