Definition
An ATC instruction directing the pilot to activate the transponder's altitude reporting feature (Mode C), so that the aircraft's pressure altitude is transmitted along with the assigned transponder code.
Plain English
Turn on the part of your transponder that sends your altitude to the controller's radar.
Context Anchor
Heard in radio instructions from air traffic control when the controller wants your transponder to report altitude on radar.
Derivation
Squawk' comes from the World War II identification system code-named 'Parrot,' so transmitting an identifying signal became known as 'squawking.' The word stuck and is now standard ATC phraseology for transponder instructions.
Why Pilots Care
Allows ATC to maintain vertical separation and issue accurate traffic advisories.
Intuition Check
SQUAWK Altitude does not mean say your altitude on the radio. It means turn on altitude reporting in the transponder.
Example Sentence 1
Cessna 12345, squawk altitude.
Example Sentence 2
After departure the pilot was instructed to squawk altitude and ident.