Plain English Meaning
ATC is telling you to set your transponder to the Standby setting. The transponder stays on but stops sending replies to radar until you switch it back to an active mode.
Full Definition
An ATC instruction directing the pilot to switch the transponder to the Standby (SBY) mode. In Standby, the transponder is powered on and warming up but does not reply to radar interrogations, so the aircraft will not display a beacon return on the controller's radar.
Context Anchor
Heard in ATC radio communications when a controller wants the aircraft transponder temporarily stopped or reset from active use.
Derivation
‘Squawk’ comes from the World War II identification system nicknamed ‘Parrot,’ so telling an aircraft to ‘squawk’ became shorthand for operating the transponder. ‘Standby’ here is the labeled mode position on the transponder itself.