Definition
An action taken to transfer the radar identification of an aircraft from one controller to another controller, accompanied by the transfer of communications and control responsibility for the aircraft.
Plain English
When one air traffic controller passes you to the next controller, they coordinate so the next controller knows exactly which target on radar is you, then tell you to switch to the new frequency. Your control passes from one controller to the next without losing track of you.
Context Anchor
Seen in instrument flying discussions of control sequence and trim, especially when checking whether the airplane will hold the desired attitude without constant control pressure.
Derivation
Hand-off comes from the literal idea of having the hand off the control. In this context it points to relief of control pressure, not to giving something to another person.
Why Pilots Care
A smooth hand-off keeps continuous radar coverage and communication so separation from other traffic is never lost.
Intuition Check
Do not confuse hand-off here with an air traffic control handoff. Here it means the pilot is not having to hold continuous pressure on the flight controls.
Example Sentence 1
After the hand-off from Departure, the pilot checked in with Center and was given a direct routing to the next fix.
Example Sentence 2
Center initiated a hand-off to the next sector before we reached the boundary.