Plain English Meaning
A tiny gear attached to the same shaft as the airspeed needle. When the gear turns, the needle turns with it.
Full Definition
A small toothed gear inside an airspeed indicator that is fixed to the shaft carrying the indicator needle. As the instrument's mechanism rotates a larger gear (the sector), its teeth turn the handstaff pinion, which in turn rotates the needle across the dial face.
Context Anchor
Seen in diagrams of the inside of a mechanical airspeed indicator, such as Figure 5-11 in the Instrument Flying Handbook.
Derivation
Handstaff' comes from the German Uhrmacher tradition meaning the staff (shaft) that carries the hand (needle) of an instrument. 'Pinion' comes from the French 'pignon,' meaning a small gear that meshes with a larger one. Together it means 'the small gear on the needle's shaft.'