Plain English Meaning
It's the set of parts that connects your feet on the rudder pedals to the front wheel, so pressing a pedal turns the nose of the airplane on the ground.
Full Definition
The mechanical connection between the rudder pedals and the nosewheel that allows the pilot to steer the airplane on the ground by pressing the rudder pedals. In most light airplanes the linkage uses push-pull rods or springs that turn the nosewheel left or right in response to pedal input.
Context Anchor
You encounter this term during taxiing discussions, preflight checks near the nosewheel, and any situation where the airplane’s ground steering is being described.
Derivation
Linkage' comes from '' -- a connecting piece. In mechanical terms, a linkage is a series of parts that pass motion from one place to another. Here, it passes motion from the rudder pedals to the nosewheel.